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  • 1.
    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. Spectral Estimates for L-1-potentials and an Ambartsumian Theorem2018In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 90, no 3, article id 40Article in journal (Refereed)
    Abstract [en]

    In this paper we study Schrodinger operators with absolutely integrable potentials on metric graphs. Uniform bounds-i.e. depending only on the graph and the potential-on the difference between the eigenvalues of the Laplace and Schrodinger operators are obtained. This in turn allows us to prove an extension of the classical Ambartsumian Theorem which was originally proven for Schrodinger operators with Neumann conditions on an interval. We also extend a previous result relating the spectrum of a Schrodinger operator to the Euler characteristic of the underlying metric graph.

  • 2.
    Kurasov, Pavel
    Stockholm University.
    H_-n-perturbations of self-adjoint operators and Krein's resolvent formula2003In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989Article in journal (Refereed)
  • 3.
    Kurasov, Pavel
    et al.
    Stockholm University.
    Albeverio, Sergio
    Rank one perturbations of not semibounded operators1997In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989Article in journal (Refereed)
  • 4.
    Kurasov, Pavel
    et al.
    Stockholm University.
    Dijksma, Aad
    Shondin, Yuri
    High order singular rank one perturbations of a positive operator2005In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989Article in journal (Refereed)
  • 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.

  • 6.
    Rohleder, Jonathan
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Seifert, Christian
    Absolutely Continuous Spectrum for Laplacians on Radial Metric Trees and Periodicity2017In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 89, no 3, p. 439-453Article in journal (Refereed)
  • 7.
    Stampach, Frantisek
    Stockholm University, Faculty of Science, Department of Mathematics. Czech Technical University in Prague, Czech Republic.
    The Characteristic Function for Complex Doubly Infinite Jacobi Matrices2017In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 88, no 4, p. 501-534Article in journal (Refereed)
    Abstract [en]

    We introduce a class of doubly infinite complex Jacobi matrices determined by a simple convergence condition imposed on the diagonal and off-diagonal sequences. For each Jacobi matrix belonging to this class, an analytic function, called a characteristic function, is associated with it. It is shown that the point spectrum of the corresponding Jacobi operator restricted to a suitable domain coincides with the zero set of the characteristic function. Also, coincidence regarding the order of a zero of the characteristic function and the algebraic multiplicity of the corresponding eigenvalue is proved. Further, formulas for the entries of eigenvectors, generalized eigenvectors, a summation identity for eigenvectors, and matrix elements of the resolvent operator are provided. The presented method is illustrated by several concrete examples.

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