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  • 1.
    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.

  • 2.
    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.

  • 3. 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.

  • 4.
    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.

  • 5.
    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.

  • 6.
    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.

  • 7.
    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, 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.

  • 8.
    Bandmann, Olav
    Stockholm University, Faculty of Science.
    A boundary for groups1995Doctoral thesis, monograph (Other academic)
  • 9.
    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)
  • 10. 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.

  • 11.
    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)
  • 12.
    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.

  • 13.
    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.

  • 14.
    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.

  • 15.
    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.

  • 16.
    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.

  • 17.
    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.

  • 18.
    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.

  • 19.
    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)
  • 20.
    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.))
  • 21.
    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)
  • 22.
    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)
  • 23. 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.

  • 24.
    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.

  • 25. 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.

  • 26. 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.

  • 27.
    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)
  • 28.
    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)
  • 29.
    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)
  • 30.
    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)
  • 31.
    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.

  • 32.
    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)
  • 33.
    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)
  • 34. Clapp, Mónica
    et al.
    Szulkin, Andrzej
    Stockholm University, Faculty of Science, Department of Mathematics.
    A Supercritical Elliptic Problem in a Cylindrical Shell2014In: Analysis and Topology in Nonlinear Differential Equations: A Tribute to Bernhard Ruf on the Occasion of his 60th Birthday / [ed] de Figueiredo et al, Basel: Birkhäuser , 2014, p. 233-242Chapter in book (Refereed)
    Abstract [en]

    We consider the problem \[-\Delta u=\left\vert u\right\vert ^{p-2}u\text{ \ in }\Omega,\quad u=0\text{\ on }\partial\Omega,\]where $\Omega:=\{(y,z)\in\mathbb{R}^{m+1}\times\mathbb{R}^{N-m-1}%:0<a<\left\vert y\right\vert <b<\infty\}$, $0\leq m\leq N-1$ and $N\geq2.$ Let$2_{N,m}^{\ast}:=2(N-m)/(N-m-2)$ if $m<N-2$ and $2_{N,m}^{\ast}:=\infty$ if$m=N-2$ or $N-1.$ We show that $2_{N,m}^{\ast}$ is the true critical exponent forthis problem, and that there exist nontrivial solutions if $2<p<2_{N,m}^{\ast}$ butthere are no such solutions if $p\geq2_{N,m}^{\ast}$.

  • 35.
    Clapp, Mónica
    et al.
    Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico.
    Szulkin, Andrzej
    Stockholm University, Faculty of Science, Department of Mathematics.
    Multiple solutions to a nonlinear Schrödinger equation with Aharonov-Bohm magnetic potential2010In: NoDEA. Nonlinear differential equations and applications (Printed ed.), ISSN 1021-9722, E-ISSN 1420-9004, Vol. 17, no 2, p. 229-248Article in journal (Refereed)
  • 36. Derks, Gianne
    et al.
    Maad, Sara
    Stockholm University, Faculty of Science, Department of Mathematics. matematik.
    Sandstede, Björn
    Perturbations of embedded eigenvalues for the bilaplacian on a cylinder2008In: Discrete and Continuous Dynamical Systems: Series A, ISSN 1078-0947, Vol. 21, no 3, p. 801-821Article in journal (Refereed)
  • 37. Derks, Gianne
    et al.
    Maad Sasane, Sara
    Stockholm University, Faculty of Science, Department of Mathematics.
    Sandstede, Björn
    Perturbations of embedded eigenvalues for the planar bilaplacian2011In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 260, no 2, p. 340-398Article in journal (Refereed)
    Abstract [en]

    Operators on unbounded domains may acquire eigenvalues that are embedded in the essential spectrum. Determining the fate of these embedded eigenvalues under small perturbations of the underlying operator is a challenging task, and the persistence properties of such eigenvalues are linked intimately to the multiplicity of the essential spectrum. In this paper, we consider the planar bilaplacian with potential and show that the set of potentials for which an embedded eigenvalue persists is locally an infinite-dimensional manifold with infinite codimension in an appropriate space of potentials.

  • 38. Ding, Yanheng
    et al.
    Szulkin, Andrzej
    Stockholm University, Faculty of Science, Department of Mathematics. matematik.
    Bound states for semilinear Schrödinger equations with sign-changing potential2007In: Calculus of variations, Vol. 29, p. 397-419Article in journal (Refereed)
    Abstract [en]

    We study the existence and the number of decaying solutions for the semilinear Schr\"odinger equations $-\eps^2\Delta u + V(x)u = g(x,u)$, $\eps>0$ small, and $-\Delta u + \la V(x)u = g(x,u)$, $\la>0$ large. The potential $V$ may change sign and $g$ is either asymptotically linear or superlinear (but subcritical) in $u$ as $|u|\to\infty$.

  • 39.
    Fredholm, Daniel
    Stockholm University, Faculty of Science.
    Intensional aspects of function definitions1994Doctoral thesis, monograph (Other academic)
  • 40.
    Holme, Petter
    Stockholm University, Faculty of Social Sciences, Department of Sociology. Umeå University, Sweden; Sungkyunkwan University, South Korea.
    Epidemiologically Optimal Static Networks from Temporal Network Data2013In: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 9, no 7, article id e1003142Article in journal (Refereed)
    Abstract [en]

    One of network epidemiology's central assumptions is that the contact structure over which infectious diseases propagate can be represented as a static network. However, contacts are highly dynamic, changing at many time scales. In this paper, we investigate conceptually simple methods to construct static graphs for network epidemiology from temporal contact data. We evaluate these methods on empirical and synthetic model data. For almost all our cases, the network representation that captures most relevant information is a so-called exponential-threshold network. In these, each contact contributes with a weight decreasing exponentially with time, and there is an edge between a pair of vertices if the weight between them exceeds a threshold. Networks of aggregated contacts over an optimally chosen time window perform almost as good as the exponential-threshold networks. On the other hand, networks of accumulated contacts over the entire sampling time, and networks of concurrent partnerships, perform worse. We discuss these observations in the context of the temporal and topological structure of the data sets.

  • 41. Jalilian, Yaghoub
    et al.
    Szulkin, Andrzej
    Stockholm University, Faculty of Science, Department of Mathematics.
    Infinitely many solutions for semilinear elliptic problems with sign-changing weight functions:  2014In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, no 4, p. 756-770Article in journal (Refereed)
    Abstract [en]

    In this paper we study the elliptic problem\begin{equation*} \left\{\begin{array}{ll} -\Delta u+u = a(x)|u|^{p-2}u+b(x)|u|^{q-2}u,\\ u\in H^{1}(\mathbb{R}^{N}),\end{array}\right.\end{equation*}where $2^{*}$ is the critical Sobolev exponent, $2< p<q< 2^{*}$and $a$ or $b$ is a sign-changing function. Under different assumptions on $a$ and $b$ we prove the existenceof infinitely many solutions to the above problem. We also show that one of these solutions is positive.

  • 42.
    Johansson, Petter
    Stockholm University, Faculty of Science, Department of Mathematics.
    On the topology of the coamoeba2014Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis we study the topology and geometry of the coamoeba of an algebraic variety V. The strategy that we use is to relate the coamoebas corresponding to the initial varieties of V to the coamoeba of V. We also define an analogue of the Ronkin function for the coamoeba and give an explicit formula for it.

  • 43.
    Johansson, Petter
    Stockholm University.
    Some results on amoebas and coamoebas of affine spacesManuscript (preprint) (Other academic)
  • 44.
    Johansson, Petter
    et al.
    Stockholm University.
    Samuelsson, Håkan
    A Ronkin type function for coamoebasManuscript (preprint) (Other academic)
  • 45. Katkova, Olga
    et al.
    Shapiro, Boris
    Stockholm University, Faculty of Science, Department of Mathematics.
    Vishnyakova, Anna
    MULTIPLIER SEQUENCES AND LOGARITHMIC MESH2011In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 349, no 1-2, p. 35-38Article in journal (Refereed)
    Abstract [en]

    In this note we prove a new result about (finite) multiplier sequences, i.e. linear operators acting diagonally in the standard monomial basis of R[x] and sending polynomials with all real roots to polynomials with all real roots. Namely, we show that any such operator does not decrease the logarithmic mesh when acting on an arbitrary polynomial having all roots real and of the same sign. The logarithmic mesh of such a polynomial is defined as the minimal quotient of its consecutive roots taken in the nondecreasing order of their absolute values.

  • 46. Kostov, Vladimir P.
    et al.
    Shapiro, Boris
    Stockholm University, Faculty of Science, Department of Mathematics.
    Tyaglov, Mikhail
    MAXIMAL UNIVALENT DISKS OF REAL RATIONAL FUNCTIONS AND HERMITE-BIEHLER POLYNOMIALS2011In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 139, no 5, p. 1625-1635Article in journal (Refereed)
    Abstract [en]

    The well-known Hermite-Biehler theorem claims that a univariate monic polynomial s of degree k has all roots in the open upper half-plane if and only if s = p + iq, where p and q are real polynomials of degree k and k - 1 respectively with all real, simple and interlacing roots, and q has a negative leading coefficient. Considering roots of p as cyclically ordered on RP1 we show that the open disk in CP1 having a pair of consecutive roots of p as its diameter is the maximal univalent disk for the function R = q/p. This solves a special case of the so-called Hermite-Biehler problem.

  • 47.
    Kostov, Vladimir
    et al.
    Dept. of Mathematics, Univ. de Nice.
    Shapiro, Boris
    Stockholm University, Faculty of Science, Department of Mathematics.
    On the Schur-Szegö composition of polynomials2006In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 343, no 2, p. 81-86Article in journal (Refereed)
    Abstract [en]

    The Schur-Szeg¨o composition of two polynomials of degree   n introduces an interesting semigroup structure on polynomial spaces and is one of the basic tools in the analytic theory of polynomials, see [5]. In the present paper we show how it interacts with the stratification of polynomials according to the multiplicities of their zeros and we present the induced semigroup structure on the set of all ordered partitions of n. 

  • 48.
    Kryszewski, Wojciech
    et al.
    Department of Mathematics, Nicholas Copernicus University, Torun, Poland.
    Szulkin, Andrzej
    Stockholm University, Faculty of Science, Department of Mathematics. Matematik.
    Infinite-dimensional homology and multibump solutions2009In: Journal of Fixed Point Theory and Applications, ISSN 1661-7738, Vol. 5, no 1, p. 33p. 1-35Article in journal (Refereed)
    Abstract [en]

    We start by introducing a Cech homology with compact supports which we then use in order to construct an infinite-dimensional homology theory. Next we show that under appropriate conditions on the nonlinearity there exists a ground state solution for a semilinear Schrödinger equation with strongly indefinite linear part. To this solution there corresponds a nontrivial critical group, defined in terms of the infinite-dimensional homology mentioned above. Finally we employ this fact in order to construct solutions of multibump type. Although our main purpose is to survey certain homological methods in critical point theory, we also include some new results.

  • 49.
    Kurasov, Pavel
    Stockholm University, Faculty of Science, Department of Mathematics.
    Spectral Gap for Complete Graphs: Upper and Lower Estimates2015Report (Other academic)
    Abstract [en]

    Lower and upper estimates for the spectral of the Laplacian on a compact metric graph are discussedà New upper estimates are presented and existing lower estimates are reviewedà The accuracy of these estimates is checked in the case of complete not necessarily regular graph with large number of vertices.

  • 50.
    Kurasov, Pavel
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Karreskog, Gustav
    Stockholm University, Faculty of Science, Department of Mathematics.
    Trygg Kupersmidt, Isak
    Stockholm University, Faculty of Science, Department of Mathematics.
    Schrödinger operators on graphs: symmetrization and Eulerian cycles2015Report (Other academic)
    Abstract [en]

    Spectral properties of the Schrödinger operator on a finite compact metric graph with delta-type vertex conditions are discussed. Explicit estimates for the lowest eigenvalue (ground state) are obtained using two different methods:Eulerian cycle and symmetrization techniques. In the case of positive interactions even estimates for higher eigenvalues are derived.

12 1 - 50 of 93
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