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  • 1. Agmon, Shmuel
    et al.
    Herbst, Ira
    Maad Sasane, Sara
    Stockholm University, Faculty of Science, Department of Mathematics.
    Persistence of embedded eigenvalues2011In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 261, no 2, p. 451-477Article in journal (Refereed)
    Abstract [en]

    We consider conditions under. which an embedded eigenvalue of a self-adjoint operator remains embedded under small perturbations. In the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m < infinity we show that in favorable situations, the set of small perturbations of a suitable Banach space which do not remove the eigenvalue form a smooth submanifold of codimension in. We also have results regarding the cases when the eigenvalue is degenerate or when the multiplicity of the continuous spectrum is infinite.

  • 2. 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)
  • 3. 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.

  • 4.
    Lasiecka, Irena
    et al.
    University of Virginia, Department of Mathematics.
    Maad, Sara
    Stockholm University, Faculty of Science, Department of Mathematics.
    Sasane, Amol
    London School of Economics, Department of Mathematics.
    Existence and exponential decay of solutions to a quasilinear thermoelastic plate system2008In: NoDEA. Nonlinear differential equations and applications (Printed ed.), ISSN 1021-9722, E-ISSN 1420-9004, Vol. 15, no 6, p. 689-715Article in journal (Refereed)
    Abstract [en]

    We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in , n ≤ 3. Existence of finite energy solutions describing the dynamics of a nonlinear thermoelastic plate is established. In addition asymptotic long time behavior of weak solutions is discussed. It is shown that finite energy solutions decay exponentially to zero with the rate depending only on the (finite energy) size of initial conditions. The proofs are based on methods of weak compactness along with nonlocal partial differential operator multipliers which supply the sought after “recovery” inequalities. Regularity of solutions is also discussed by exploiting the underlying analyticity of the linearized semigroup along with a related maximal parabolic regularity.

  • 5.
    Maad Sasane, Sara
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Sasane, Amol
    Generators for rings of compactly supported distributions2011In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 69, no 1, p. 63-71Article in journal (Refereed)
    Abstract [en]

    Let CUnknown control sequence '\tt' denote a closed convex cone in \mathbb RdRd with apex at 0. We denote by E¢(C)Unknown control sequence '\tt' the set of distributions on \mathbb RdRd having compact support contained in CUnknown control sequence '\tt'. Then E¢(C)Unknown control sequence '\tt' is a ring with the usual addition and with convolution. We give a necessary and sufficient analytic condition on [^(f)]1,..., [^(f)]nf1fn for f1,... ,fn Î E¢(C)Unknown control sequence '\tt' to generate the ring E¢(C)Unknown control sequence '\tt'. (Here [^(  ·  )] denotes Fourier-Laplace transformation.) This result is an application of a general result on rings of analytic functions of several variables by Lars Hörmander. En route we answer an open question posed by Yutaka Yamamoto.

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