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  • 1. Abatangelo, Laura
    et al.
    Felli, Veronica
    Hillairet, Luc
    Léna, Corentin
    Stockholm University, Faculty of Science, Department of Mathematics.
    Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators2019In: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403, Vol. 9, no 2, p. 379-427Article in journal (Refereed)
    Abstract [en]

    We first establish a sharp relation between the order of vanishing of a Dirichlet eigenfunction at a point and the leading term of the asymptotic expansion of the Dirichlet eigenvalue variation, as a removed compact set concentrates at that point. Then we apply this spectral stability result to the study of the asymptotic behaviour of eigenvalues of Aharonov–Bohm operators with two colliding poles moving on an axis of symmetry of the domain.

  • 2. Abatangelo, Laura
    et al.
    Felli, Veronica
    Léna, Corentin
    Stockholm University, Faculty of Science, Department of Mathematics.
    Eigenvalue variation under moving mixed Dirichlet–Neumann boundary conditions and applications2020In: ESAIM: Control, Optimisation and Calculus of Variations , ISSN 1292-8119, E-ISSN 1262-3377, Vol. 26, article id 39Article in journal (Refereed)
    Abstract [en]

    We deal with the sharp asymptotic behaviour of eigenvalues of elliptic operators with varying mixed Dirichlet–Neumann boundary conditions. In case of simple eigenvalues, we compute explicitly the constant appearing in front of the expansion’s leading term. This allows inferring some remarkable consequences for Aharonov–Bohm eigenvalues when the singular part of the operator has two coalescing poles.

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  • 3.
    Aldeghi, Nausica
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Rohleder, Jonathan
    Stockholm University, Faculty of Science, Department of Mathematics.
    Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions2023In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 524, no 1, article id 127078Article in journal (Refereed)
    Abstract [en]

    The eigenvalue problem for the Laplacian on bounded, planar, convex domains with mixed boundary conditions is considered, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its complement. Given two different such choices of boundary conditions for the same domain, we prove inequalities between their lowest eigenvalues. As a special case, we prove parts of a conjecture on the order of mixed eigenvalues of triangles.

  • 4.
    Alexandersson, Per
    Stockholm University, Faculty of Science, Department of Mathematics.
    On eigenvalues of the Schrödinger operator with a complex-valued polynomial potential2010Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis, we generalize a recent result of A. Eremenko and A. Gabrielov on irreducibility of the spectral discriminant for the Schroedinger equation with quartic potentials.

    In the first paper, we consider the eigenvalue problem with a complex-valued polynomial potential of arbitrary degree d and show that the spectral determinant of this problem is connected and irreducible. In other words, every eigenvalue can be reached from any other by analytic continuation. We also prove connectedness of the parameter spaces of the potentials that admit eigenfunctions satisfying k > 2 boundary conditions, except for the case d is even and k = d/2. In the latter case, connected components of the parameter space are distinguished by the number of zeros of the eigenfunctions.

    In the second paper, we only consider even polynomial potentials, and show that the spectral determinant for the eigenvalue problem consists of two irreducible components. A similar result to that of paper I is proved for k boundary conditions.

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  • 5.
    Arias, Sergi
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Rodriguez-Lopez, Salvador
    Stockholm University, Faculty of Science, Department of Mathematics.
    Bilinear pseudodifferential operators with symbol in BSm1,1 on Triebel-Lizorkin spaces with critical Sobolev index2023In: Collectanea Mathematica (Universitat de Barcelona), ISSN 0010-0757, E-ISSN 2038-4815Article in journal (Refereed)
    Abstract [en]

    In this paper we obtain new estimates for bilinear pseudodiferential operators with symbol in the class , when both arguments belong to Triebel-Lizorkin spaces of the type . The inequalities are obtained as a consequence of a refnement of the classical Sobolev embedding ↪bmo(ℝn), where we replace bmo(ℝn) by an appropriate subspace which contains L(ℝn). As an application, we study the product of functions on when 1 < p < ∞, where those spaces fail to be multiplicative algebras.

  • 6.
    Arias, Sergi
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Rodríguez-López, Salvador
    Stockholm University, Faculty of Science, Department of Mathematics.
    Endpoint Estimates For Bilinear Pseudodifferential Operators With Symbol In Bs1,1M2022In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 515, no 1, article id 126453Article in journal (Refereed)
    Abstract [en]

    In this paper we establish some endpoint estimates for bilinear pseudodifferential operators with symbol in the class BS, involving the space of functions with local bounded mean oscillation bmo(Rn). As a consequence we also obtain an endpoint estimate of Kato-Ponce type.

  • 7.
    Arioli, Gianni
    et al.
    Dipartimento di Matematica, Politecnico di Milano, Milano, Italy.
    Szulkin, Andrzej
    Stockholm University, Faculty of Science, Department of Mathematics. matematik.
    Zou, Wenming
    Department of Mathematical Sciences, Tsinghua University, Beijing, China.
    Multibump solutions and critical groups2009In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 361, no 6, p. 33p. 3159-3187Article in journal (Refereed)
    Abstract [en]

    We consider the Newtonian system $-\ddot q+B(t)q = W_q(q,t)$ with $B$, $W$ periodic in $t$, $B$ positive definite, and show that for each isolated homoclinic solution $q_0$ having a nontrivial critical group (in the sense of Morse theory) multibump solutions (with $2\le k\le\iy$ bumps) can be constructed by gluing translates of $q_0$. Further we show that the collection of multibumps is semiconjugate to the Bernoulli shift. Next we consider the Schr\"odinger equation $-\Delta u+V(x)u = g(x,u)$ in $\RN$, where $V$, $g$ are periodic in $x_1,\ldots,x_N$, $\sigma(-\Delta+V)\subset (0,\iy)$, and we show that similar results hold in this case as well. In particular, if $g(x,u)=|u|^{2^*-2}u$, $N\ge 4$ and $V$ changes sign, then there exists a solution minimizing the associated functional on the Nehari manifold. This solution gives rise to multibumps if it is isolated.

  • 8. Astudillo, Maria
    et al.
    Kurasov, Pavel
    Stockholm University, Faculty of Science, Department of Mathematics.
    Usman, Muhammad
    Stockholm University, Faculty of Science, Department of Mathematics.
    RT-symmetric Laplace operators on star graphs: real spectrum and self-adjointness2015Report (Other academic)
    Abstract [en]

    In the current article it is analyzed how ideas of PT-symmetricquantum mechanics can be applied to quantum graphs, in particular tothe star graph. The class of rotationally-symmetric vertex conditionsis analyzed. It is shown that all such conditions can effectively be described bycirculant  matrices: real in the case of odd number of edges and complex having particular block structure  in the even case. Spectral properties of thecorresponding operators are discussed.

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  • 9.
    Axelsson, Andreas
    Stockholm University, Faculty of Science, Department of Mathematics. Matematik.
    Non unique solutions to boundary value problems for non symmetric divergence form equations2007In: Transactions of the American Mathematical Society, ISSN 0002-9947Article in journal (Refereed)
    Abstract [sv]

    We calculate explicitly solutions to the Dirichlet and Neumann boundary value problems in the upper half plane, for a family of divergence form equations with non symmetric coefficients with a jump discontinuity. It is shown that the boundary equation method and the Lax--Milgram method for constructing solutions may give two different solutions when the coefficients are sufficiently non symmetric.

  • 10.
    Axelsson, Andreas
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Alfonseca, M. Angeles
    Auscher, Pascal
    Hofmann, Steve
    Seick, Kim
    Analyticity of layer potentials and $L^{2}$ solvability of boundary value problems for divergence form elliptic equations with complex $L^{\infty}$ coefficients2007Other (Other academic)
    Abstract [en]

    We consider divergence form elliptic operators of the form $L=-\dv A(x)\nabla$, defined in $R^{n+1} = \{(x,t)\in R^n \times R \}$, $n \geq 2$, where the $L^{\infty}$ coefficient matrix $A$ is $(n+1)\times(n+1)$, uniformly elliptic, complex and $t$-independent. We show that for such operators, boundedness and invertibility of the corresponding layer potential operators on $L^2(\mathbb{R}^{n})=L^2(\partial\mathbb{R}_{+}^{n+1})$, is stable under complex, $L^{\infty}$ perturbations of the coefficient matrix. Using a variant of the $Tb$ Theorem, we also prove that the layer potentials are bounded and invertible on $L^2(\mathbb{R}^n)$ whenever $A(x)$ is real and symmetric (and thus, by our stability result, also when $A$ is complex, $\Vert A-A^0\Vert_{\infty}$ is small enough and $A^0$ is real, symmetric, $L^{\infty}$ and elliptic). In particular, we establish solvability of the Dirichlet and Neumann (and Regularity) problems, with $L^2$ (resp. $\dot{L}^2_1)$ data, for small complex perturbations of a real symmetric matrix. Previously, $L^2$ solvability results for complex (or even real but non-symmetric) coefficients were known to hold only for perturbations of constant matrices (and then only for the Dirichlet problem), or in the special case that the coefficients $A_{j,n+1}=0=A_{n+1,j}$, $1\leq j\leq n$, which corresponds to the Kato square root problem.

  • 11.
    Axelsson, Andreas
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics. Stockholm University, Faculty of Science, Department of Mathematics. matematik.
    Auscher, Pascal
    Hofmann, Steve
    Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems2008In: Journal of functional analysis, ISSN 0022-1236, Vol. 255, no 2, p. 374-448Article in journal (Refereed)
    Abstract [en]

    We prove that the Neumann, Dirichlet and regularity problems for divergence form elliptic equations in the half space are well posed in $L_2$ for small complex $L_\infty$ perturbations of a coefficient matrix which is either real symmetric, of block form or constant. All matrices are assumed to be independent of the transversal coordinate. We solve the Neumann, Dirichlet and regularity problems through a new boundary operator method which makes use of operators in the functional calculus of an underlaying first order Dirac type operator. We establish quadratic estimates for this Dirac operator, which implies that the associated Hardy projection operators are bounded and depend continuously on the coefficient matrix. We also prove that certain transmission problems for $k$-forms are well posed for small perturbations of block matrices.

  • 12.
    Bahrami, Fariba
    et al.
    University of Tabriz, Dept. of Mathematics.
    Nycander, Jonas
    Stockholm University, Faculty of Science, Department of Meteorology .
    Alikhani, Robab
    University of Tabriz, Dept. of Mathematics.
    Existence of energy maximizing vortices in a three-dimensionalquasigeostrophic shear flow with bounded height2010In: Nonlinear Analysis: Real World Applications, ISSN 1468-1218, Vol. 11, no 3, p. 1589-1599Article in journal (Refereed)
    Abstract [en]

    The existence of an energy maximizer relative to a class of rearrangements of agiven function is proved. The maximizers are stationary and stable solutions of thequasigeostrophic equation, which governs the time evolution of large-scale threedimensionalgeophysical flow in a vertically bounded domain. The background flow isunidirectional, with linear horizontal shear. The theorem proved implies the existence of afamily of stationary and stable vortices that rotate in the same direction as the backgroundshear. It extends an earlier theorem by Burton and Nycander, which is valid for a verticallyunbounded domain.

  • 13.
    Bakas, Odysseas
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Rodríguez-López, Salvador
    Stockholm University, Faculty of Science, Department of Mathematics.
    Sola, Alana
    Stockholm University, Faculty of Science, Department of Mathematics.
    Multi-parameter extensions of a theorem of Pichorides2019In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 147, no 3, p. 1081-1095Article in journal (Refereed)
    Abstract [en]

    Extending work of Pichorides and Zygmund to the d-dimensional setting, we show that the supremum of L-p-norms of the Littlewood-Paley square function over the unit ball of the analytic Hardy spaces H-A(p) (T-d) blows up like (p-1)(-d) as p -> 1(+). Furthermore, we obtain an Llog(d) L-estimate for square functions on H-A(1) (T-d). Euclidean variants of Pichorides' theorem are also obtained.

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  • 14.
    Bandmann, Olav
    Stockholm University, Faculty of Science.
    A boundary for groups1995Doctoral thesis, monograph (Other academic)
  • 15.
    Bartsch, Thomas
    et al.
    Mathematisches Institut, Universität Giessen, Germany.
    Szulkin, Andrzej
    Stockholm University, Faculty of Science, Department of Mathematics. matematik.
    Willem, Michel
    Institut de Mathématiques Pure et Appliquée, Université Catholique de Louvain, Louvain-La-Neuve, Belgium.
    Morse theory and nonlinear differential equations2008In: Handbook of Global Analysis / [ed] D. Krupka, D. Saunders, Amsterdam: Elsevier , 2008, p. 41-73Chapter in book (Other academic)
  • 16. Behrndt, Jussi
    et al.
    Langer, Matthias
    Lotoreichik, Vladimir
    Rohleder, Jonathan
    Stockholm University, Faculty of Science, Department of Mathematics.
    Quasi boundary triples and semi-bounded self-adjoint extensions2017In: Proceedings of the Royal Society of Edinburgh. Section A Mathematics, ISSN 0308-2105, E-ISSN 1473-7124, Vol. 147, no 5, p. 895-916Article in journal (Refereed)
    Abstract [en]

    In this note semi-bounded self-adjoint extensions of symmetric operators are investigated with the help of the abstract notion of quasi boundary triples and their Weyl functions. The main purpose is to provide new sufficient conditions on the parameters in the boundary space to induce self-adjoint realizations, and to relate the decay of the Weyl function to estimates on the lower bound of the spectrum. The abstract results are illustrated with uniformly elliptic second-order partial differential equations on domains with non-compact boundaries.

  • 17. Behrndt, Jussi
    et al.
    Rohleder, Jonathan
    Stockholm University, Faculty of Science, Department of Mathematics.
    Inverse problems with partial data for elliptic operators on unbounded Lipschitz domains2020In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 36, no 3, article id 035009Article in journal (Refereed)
    Abstract [en]

    For a second order formally symmetric elliptic differential expression we show that the knowledge of the Dirichlet-to-Neumann map or Robin-to-Dirichlet map for suitably many energies on an arbitrarily small open subset of the boundary determines the self-adjoint operator with a Dirichlet boundary condition or with a (possibly non-self-adjoint) Robin boundary condition uniquely up to unitary equivalence. These results hold for general Lipschitz domains, which can be unbounded and may have a non-compact boundary, and under weak regularity assumptions on the coefficients of the differential expression.

  • 18. Bergfeldt, Aksel
    et al.
    Rodríguez-López, Salvador
    Stockholm University, Faculty of Science, Department of Mathematics.
    Rule, David
    Staubach, Wolfgang
    MULTILINEAR OSCILLATORY INTEGRALS AND ESTIMATES FOR COUPLED SYSTEMS OF DISPERSIVE PDES2023In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850Article in journal (Refereed)
    Abstract [en]

    We establish sharp global regularity of a class of multilinear oscillatory integral operators that are associated to nonlinear dispersive equations with both Banach and quasi-Banach target spaces. As a consequence we also prove the (local in time) continuous dependence on the initial data for solutions of a large class of coupled systems of dispersive partial differential equations.

  • 19.
    Bergkvist, Tanja
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics. Matematik.
    Rullgård, Hans
    Stockholm University, Faculty of Science, Department of Mathematics. Matematik.
    On polynomial eigenfunctions for a class of differential operators2002In: Mathematical research letters, Vol. 9, no 2, p. 153-171Article in journal (Refereed)
  • 20.
    Bergqvist, Linus
    Stockholm University, Faculty of Science, Department of Mathematics.
    Function spaces and rational inner functions on polydiscs2021Licentiate thesis, monograph (Other academic)
    Abstract [en]

    In this thesis we consider problems related to rational inner functionsand several different Hilbert spaces on the unit polydisc. In the general introduction the functions and the function spaces we will be interested in are introduced, and in particular we point outproblems and phenomena that occur in higher dimensions and are notpresent for one variable functions. For example, we provide a detailed construction of a non-trivial shift-invariant subspace of Dirichlet-type spaces on the bidisc which is not fnitely generated. Furthermore, Clark-Aleksandrov measures are generalized to higher dimensions, and certain results about such measures are proved.

    Paper I concerns containment of rational inner functions in Dirichlet-type spaces on polydiscs. In particular a theorem relating H^p integrability of the partial derivatives of a rational inner function to containment of the function in certain Dirichlet-type spaces is proved. As a corollary, we see that every rational inner function on D^n belongs to the isotropic Dirichlet-type space with weight 1/n. In Paper II, Zhu's sub-Bergman spaces of one variable functions on the unit disc are generalized to weighted Bergman spaces on D^n. Unlike in one variable,we show that sub-Bergman spaces associated to a rational inner function are generally not contained in a weighted Bergman space of higher regularity. We also show how Clark measures on the n-torus can be used to study model spaces on D^n associated to rational inner functions.

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  • 21.
    Bergqvist, Linus
    Stockholm University, Faculty of Science, Department of Mathematics.
    Holomorphic functions on polydiscs and measures on the distinguished boundary2023Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of four papers, treating holomorphic functions defined on polydiscs, operators acting on spaces of such functions, and related measures on the n-torus. In paper I we study containment of rational inner functions, or RIFs for short, in Dirichlet type spaces on the unit polydisc D^n. In particular, a theorem relating H^p integrability of the partial derivatives of an RIF to containment of the function in certain Dirichlet type spaces is proved. As a corollary we see that every RIF on D^n belongs to the isotropic Dirichlet type space with parameter 1/n. We also show that if ϕ = ˜p/p is an RIF on D^n with the property that 1/p lies in some isotropic Dirichlet type space with parameter α < 0, then ϕ is contained in the isotropic Dirichlet type space with parameter α + 2/n. In paper II we provide new proofs of Mandrekar’s theorem on shift invariant subspaces of the Hardy space H^2(D^2). The theorem says that an invariant subspace M of H^2(D^2) is generated by an inner function if and only if the shift operators are doubly commuting on M. The new proofs in this paper are elementary and transparent, and mainly use basic properties of reproducing kernels.In paper III we study Clark measures corresponding to RIFs on D^2. We give an explicit description of such measures when regarded as bounded linear functionals on the continuous functions on T^2, analyse when the corresponding Clark embedding operator is unitary, and relate the density of these measures to a geometric property of zero sets associated with the corresponding RIFs. In paper IV we study measures on T^n having the property that their Poisson integral is the real part of some holomorphic function on D^n: so called RP-measures. We give necessary conditions on the support of RP-measures, and among other things show that their supports cannot have linear measure zero. Furthermore, we relate failure of a set to support any positive RP-measure with uniform approximability of continuous functions by certain holomorphic functions. For n = 2 this gives us a necessary and sufficient condition for a subset of T^2 to contain the support of some positive RP-measure.

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  • 22.
    Bergqvist, Linus
    Stockholm University, Faculty of Science, Department of Mathematics.
    Necessary conditions on the support of RP-measuresManuscript (preprint) (Other academic)
    Abstract [en]

    By associating RP-measures with annihilators of A_0 – a subspace of the polydisc algebra – we provide necessary conditions for when a compact subset of T^n can contain the support of a non-zero RP-measure. Among other things we show that the support of a positive RP-measure cannot be contained in reflections of inverse images of half-planes by functions in A_0, sets of linear measure zero, and when n =2, graphs of strictly increasing functions. Furthermore, we prove that failure of a compact set S to support any positive annihilator of A_0 is equivalent to uniform approximability of all continuous functions on S by functions in A_0. For n = 2 this gives a necessary and sufficient condition for the support of positive RP-measures.

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  • 23.
    Bergqvist, Linus
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Anderson, John
    Bickel, Kelly
    Sola, Alan
    Cima, Joseph
    Clark measures for rational inner functions II: General bidegrees and higher dimensionsManuscript (preprint) (Other academic)
    Abstract [en]

    We study Clark measures associated with general two-variable rational inner functions (RIFs) on the bidisk, including those with singularities, and with general d-variable rational inner functions with no singularities. We give precise descriptions of support sets and weights for such Clark measures in terms of level sets and partial derivatives of the associated RIF. In two variables, we characterize when the associated Clark embeddings are unitary, and for generic parameter values, we relate vanishing of two-variable weights with the contact order of the associated RIF at a singularity.

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  • 24.
    Björck, Göran
    Stockholm University.
    Linear partial differential operators and generalized distributions1966Doctoral thesis, monograph (Other academic)
  • 25.
    Bodnar, Taras
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Ivasiuk, Dmytro
    Parolya, Nestor
    Schmid, Wolfgang
    Multi-period power utility optimization under stock return predictability2023In: Computational Management Science, ISSN 1619-697X, E-ISSN 1619-6988, Vol. 20, no 1, article id 4Article in journal (Refereed)
    Abstract [en]

    In this paper, we derive an analytical solution to the dynamic optimal portfolio choice problem in the case of an investor equipped with a power utility function of wealth. The results are established by solving the Bellman backward recursion under the assumption that the vector of asset returns follows a vector-autoregressive process with predictable variables. In an empirical study, the performance of the derived solution is compared with the one obtained by applying the numerical method. The comparison is performed in terms of the final wealth and its expected utility. It is documented that the application of the analytical solution to the multi-period portfolio choice problem leads to higher values of both the final wealth and the expected utility.

  • 26.
    Boman, Jan
    Stockholm University, Faculty of Science, Department of Mathematics.
    A local uniqueness theorem for  weighted Radon transforms2010In: Inverse Problems and Imaging, ISSN 1930-8337, E-ISSN 1930-8345, Vol. 4, no 4, p. 631-637Article in journal (Refereed)
    Abstract [en]

    We consider a weighted Radon transform in the plane, , where is a smooth, positive function. Using an extension of an argument of Strichartz we prove a local injectivity theorem for for essentially the same class of that was considered by Gindikin in his article in this issue.

  • 27.
    Boman, Jan
    Stockholm University, Faculty of Science, Department of Mathematics.
    Flatness of distributions vanishing on infinitely many hyperplanes2009In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 347, no 23-24, p. 1351-1354Article in journal (Refereed)
    Abstract [en]

    Let

    be a family of hyperplanes in Rn and let L0 be a limiting hyperplane of {Lk}. Let u be a distribution that satisfies a natural wave front condition and has vanishing restrictions to Lk for all k1. Then u must be flat at L0.

  • 28.
    Boman, Jan
    Stockholm University, Faculty of Science, Department of Mathematics.
    Local non-injectivity for weighted Radon transforms2011In: Contemporary Mathematics, ISSN 0271-4132, E-ISSN 1098-3627, Vol. 559, p. 39-47Article in journal (Refereed)
    Abstract [en]

    A weighted plane Radon transform $R_{\rho}$ is considered, where $\rho(x, L)$ is a smooth positive function.  It is proved that the set of weight functions $\rho$, for which the map $f \mapsto R_{\rho} f$ is not locally injective, is dense in the space of smooth positive weight functions.

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  • 29.
    Boman, Jan
    Stockholm University, Faculty of Science, Department of Mathematics.
    Mer om trianglar med given omkrets och area2007In: NormatArticle in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    Mängden av trianglar med given omkrets och area studeras.

  • 30.
    Boman, Jan
    Stockholm University, Faculty of Science, Department of Mathematics.
    On local injectivity for weighted Radon transforms2012In: The mathematical legacy of Leon Ehrenpreis / [ed] Irene Sabadini, Daniele C. Struppa, Milano: Springer Milan, 2012, p. 45-60Chapter in book (Refereed)
    Abstract [en]

    We consider a class of weighted plane generalized Radon transforms Rf(γ)=∫f(x,u(ξ,η,x))m(ξ,η,x) dx, where the curve γ=γ(ξ,η) is defined by y=u(ξ,η,x), and m(ξ,η,x) is a given positive weight function. We prove local injectivity for this transform across a given curve γ0 near a given point (x0,y0) on γ0 for classes of curves and weight functions that are invariant under arbitrary smooth coordinate transformations in the plane.

  • 31.
    Boman, Jan
    Stockholm University, Faculty of Science, Department of Mathematics.
    Support theorems for the Radon transform and Cramér-Wold theorems2007Other (Other academic)
    Abstract [en]

    This article presents extensions of the Cramér-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions imposed are sharp. The extensions build on a number of results and methods concerned with injectivity properties of the Radon transform. Using a few tools from distribution theory and Fourier analysis we show that the presented injectivity results for the Radon transform lead to Cramér-Wold type results for measures. One purpose of this article is to contribute to making known to probabilists interesting results for the Radon transform that have been developed essentially during the 1980ies and 1990ies.

  • 32.
    Boman, Jan
    Stockholm University, Faculty of Science, Department of Mathematics.
    Unique continuation of microlocally analytic distributions and injectivity theorems for the ray transform2010In: Inverse Problems and Imaging, ISSN 1930-8337, Vol. 4, no 4, p. 619-630Article in journal (Refereed)
    Abstract [en]

    Using a vanishing theorem for microlocally real analytic distributions and a theorem on flatness of a distribution vanishing on infinitely many hyperplanes we give a new proof of an injectivity theorem of Bélisle, Massé, and Ransford for the ray transform on R^n. By means of  an example we show  that this result is sharp. An extension is given where real analyticity is replaced by quasianalyticity.

  • 33.
    Boman, Jan
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Agbor, Dieudonné
    On the modulus of continuity of mappings between Euclidean spaces2010In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807Article in journal (Refereed)
  • 34.
    Boman, Jan
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Björk, Jan-Erik
    Stockholm University, Faculty of Science, Department of Mathematics.
    Fuglesangs skiftnyckel och möten i rymden2007In: Normat, ISSN 0801-3500, Vol. 55, no 2Article in journal (Other (popular science, discussion, etc.))
  • 35.
    Boman, Jan
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Kurasov, Pavel
    Stockholm University, Faculty of Science, Department of Mathematics.
    Suhr, Rune
    Stockholm University, Faculty of Science, Department of Mathematics.
    Schrödinger Operators on Graphs and Geometry II. Integrable Potentials and an Ambartsumian Theorem2016Report (Other academic)
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  • 36. Bonanno, Alfio
    et al.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Del Sordo, Fabio
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Mitra, Dhrubaditya
    Breakdown of chiral symmetry during saturation of the Tayler instability2012In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 86, no 1, p. 016313-Article in journal (Refereed)
    Abstract [en]

    We study spontaneous breakdown of chiral symmetry during the nonlinear evolution of the Tayler instability. We start with an initial steady state of zero helicity. Within linearized perturbation calculations, helical perturbations of this initial state have the same growth rate for either sign of helicity. Direct numerical simulations (DNS) of the fully nonlinear equations, however, show that an infinitesimal excess of one sign of helicity in the initial perturbation gives rise to a saturated helical state. We further show that this symmetry breaking can be described by weakly nonlinear finite-amplitude equations with undetermined coefficients which can be deduced solely from symmetry consideration. By fitting solutions of the amplitude equations to data from DNS, we further determine the coefficients of the amplitude equations.

  • 37.
    Borcea, Julius
    Stockholm University, Faculty of Science, Department of Mathematics.
    Equilibrium points of logarithmic potentials induced by positive charge distributions. I. Generalized de Bruijn-Springer relations2007In: Transactions of the American Mathematical Society, Vol. 359, p. 3209-3237Article in journal (Refereed)
  • 38. Borcea, Julius
    et al.
    Friedland, Shmuel
    Shapiro, Boris
    Stockholm University, Faculty of Science, Department of Mathematics.
    Parametric Poincaré-Perron theorem with applications2011In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 113, no 1, p. 197-225Article in journal (Refereed)
    Abstract [en]

    We prove a parametric generalization of the classical Poincar´e- Perron theorem on stabilizing recurrence relations where we assume that the varying coefficients of a recurrence depend on auxiliary parameters and converge uniformly in these parameters to their limiting values. As an application we study convergence of the ratios of families of functions satisfying finite recurrence relations with varying functional coefficients. For example, we explicitly describe the asymptotic ratio for two classes of biorthogonal polynomials introduced by Ismail and Masson.

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  • 39.
    Brahme, Anders
    et al.
    Stockholm University, Faculty of Science, Medical Radiation Physics (together with KI).
    Roos, Jan-Erik
    Department of Mathematics. matematik.
    Lax, Ingemar
    Stockholm University, Faculty of Science, Medical Radiation Physics (together with KI).
    Solution of an integral equation encountered in rotation therapy1982In: Physics in Medicine and Biology, ISSN 0031-9155, Vol. 27, no 10, p. 1221-1229Article in journal (Refereed)
    Abstract [en]

    An integral equation relating the lateral absorbed dose profile of a photon beam to the resultant absorbed dose distribution during single-turn rotating-beam therapy has been set up and solved for the case of a cylindrical phantom with the axis of rotation coinciding with the axis of symmetry of the cylinder. In the first approximation the results obtained are also valid when the axis of rotation is somewhat off-centred, even in a phantom that deviates from circular symmetry, provided the rotation is performed in both clockwise and counter clockwise directions. The calculated dose profiles indicate that improved dose uniformity can be achieved using a new type of non-linear wedge-shaped filter, which can easily be designed using the derived general analytic solution to the integral equation.

  • 40. Budroni, Costantino
    et al.
    Cabello, Adan
    Stockholm University, Faculty of Science, Department of Physics.
    Bell inequalities from variable-elimination methods2012In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, no 38, p. 385304-Article in journal (Refereed)
    Abstract [en]

    Tight Bell inequalities are facets of Pitowsky's correlation polytope and are usually obtained from its extreme points by solving the hull problem. Here, we present an alternative method based on a combination of algebraic results on extensions of measures and variable-elimination methods, e. g., the Fourier-Motzkin method. Our method is shown to overcome some of the computational difficulties associated with the hull problem in some non-trivial cases. Moreover, it provides an explanation for the arising of only a finite number of families of Bell inequalities in measurement scenarios where one experimenter can choose between an arbitrary number of different measurements.

  • 41. Bénéteau, Catherine
    et al.
    Khavinson, Dmitry
    Liaw, Constanze
    Seco, Daniel
    Sola, Alan A.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants2016In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. 94, no 3, p. 726-746Article in journal (Refereed)
    Abstract [en]

    We study connections between orthogonal polynomials, reproducing kernel functions, and polynomials p minimizing Dirichlet-type norms vertical bar pf-1 vertical bar for a given function f. For [0,1] (which includes the Hardy and Dirichlet spaces of the disk) and general f, we show that such extremal polynomials are non-vanishing in the closed unit disk. For negative, the weighted Bergman space case, the extremal polynomials are non-vanishing on a disk of strictly smaller radius, and zeros can move inside the unit disk. We also explain how dist D(1,fPn), where Pn is the space of polynomials of degree at most n, can be expressed in terms of quantities associated with orthogonal polynomials and kernels, and we discuss methods for computing the quantities in question.

  • 42. Bénéteau, Catherine
    et al.
    Knese, Greg
    Kosinski, Lukasz
    Liaw, Constanze
    Seco, Daniel
    Sola, Alan
    Stockholm University, Faculty of Science, Department of Mathematics.
    Cyclic polynomials in two variables2016In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 368, no 12, p. 8737-8754Article in journal (Refereed)
    Abstract [en]

    We give a complete characterization of polynomials in two com-plex variables that are cyclic with respect to the coordinate shifts acting onDirichlet-type spaces in the bidisk, which include the Hardy space and theDirichlet space of the bidisk. The cyclicity of a polynomial depends on boththe size and nature of the zero set of the polynomial on the distinguishedboundary. The techniques in the proof come from real analytic function the-ory, determinantal representations for polynomials, and harmonic analysis oncurves.

  • 43.
    Bögvad, Rikard
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Borcea, Julius
    Stockholm University, Faculty of Science, Department of Mathematics.
    Piecewise harmonic functions and positive Cauchy transforms2009In: Pacific Journal of Mathematics, ISSN 0030-8730, E-ISSN 1945-5844, Vol. 240, no 2, p. 231-265Article in journal (Refereed)
  • 44.
    Börjeson, Lennart
    Stockholm University, Faculty of Science, Department of Mathematics.
    Estimates for the Bochner-Riesz operator with negative index.1986In: Indiana University Mathematics Journal, ISSN 0022-2518, Vol. 35, no 2, p. 225-233Article in journal (Refereed)
  • 45.
    Börjeson, Lennart
    Stockholm University, Faculty of Science, Department of Mathematics.
    Mixed norm estimates for certain means.1988In: Transactions of the American Mathematical Society, ISSN 1088-6850, Vol. 309, no 2, p. 517-541Article in journal (Refereed)
  • 46.
    Börjeson, Lennart
    Stockholm University, Faculty of Science, Department of Mathematics.
    Regularity of averages over hypersurfaces.1989In: Arkiv för Matematik, ISSN 0004-2080, Vol. 27, no 2, p. 189-210Article in journal (Refereed)
  • 47.
    Carro, María
    et al.
    Universitat de Barcelona, Spain.
    Rodriguez, Salvador
    Universitat de Barcelona, Spain.
    New results on restriction of Fourier multipliers2010In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 265, no 2, p. 417-435Article in journal (Refereed)
    Abstract [en]

    We develop an extension of the Transference methods introduced by R. Coifman and G. Weiss and apply it to study the problem of the restriction of Fourier multipliers between rearrangement invariant spaces, obtaining natural extensions of the classical de Leeuw’s result and its further extension to maximal Fourier multipliers due to C. Kenig and P. Tomas.

  • 48.
    Chabrowski, Jan
    et al.
    Department of Mathematics, University of Queensland, St. Lucia, Qld, Australia.
    Szulkin, Andrzej
    Stockholm University, Faculty of Science, Department of Mathematics. matematik.
    Willem, Michel
    Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.
    Schrödinger equation with multiparticle potential and critical nonlinearity2009In: Topological Methods in Nonlinear Analysis, ISSN 1230-3429, Vol. 34, no 2, p. 11p. 201-211Article in journal (Refereed)
  • 49.
    Clapp, Mónica
    et al.
    Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico.
    Iturriaga, Renato
    Centro de Investigación en Matemáticas, Guanajuato, Mexico.
    Szulkin, Andrzej
    Stockholm University, Faculty of Science, Department of Mathematics. Matematik.
    Periodic and Bloch solutions to a magnetic nonlinear Schrödinger equation2009In: Advanced Nonlinear Studies, ISSN 1536-1365, E-ISSN 2169-0375, Vol. 9, no 4, p. 28p. 639-655Article in journal (Refereed)
  • 50. Clapp, Mónica
    et al.
    Saldaña, Alberto
    Szulkin, Andrzej
    Stockholm University.
    Configuration spaces and multiple positive solutions to a singularly perturbed elliptic systemIn: ISSN 1405-213XArticle in journal (Refereed)
    Abstract [en]

    We consider a weakly coupled singularly perturbed variational elliptic system in a bounded smooth domain with Dirichlet boundary conditions.  We show that, in the competitive regime, the number of fully nontrivial solutions with nonnegative components increases with the number of equations. Our proofs use a combination of four key elements: a convenient variational approach, the asymptotic behavior of solutions (concentration), the Lusternik-Schnirelman theory, and new estimates on the category of suitable configuration spaces. 

123 1 - 50 of 139
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