Singular Perturbations of Self-Adjoint Operators View Full Text


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Article Info

DATE

2003-04

AUTHORS

Vladimir Derkach, Seppo Hassi, Henk de Snoo

ABSTRACT

Singular finite rank perturbations of an unbounded self-adjoint operator A0 in a Hilbert space ℌ0 are defined formally as A(α)=A0+GαG*, where G is an injective linear mapping from ℋ=ℂd to the scale space ℌ-k(A0)k ∈ ℕ, k∈N, of generalized elements associated with the self-adjoint operator A0, and where α is a self-adjoint operator in ℋ. The cases k=1 and k=2 have been studied extensively in the literature with applications to problems involving point interactions or zero range potentials. The scalar case with k=2n>1 has been considered recently by various authors from a mathematical point of view. In this paper, singular finite rank perturbations A(α) in the general setting ran G⊂ ℌ−k(A0), k∈N, are studied by means of a recent operator model induced by a class of matrix polynomials. As an application, singular perturbations of the Dirac operator are considered. More... »

PAGES

349-384

References to SciGraph publications

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  • 1997-12. Rank one perturbations of not semibounded operators in INTEGRAL EQUATIONS AND OPERATOR THEORY
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  • 1988-03. Quantum-mechanical models in Rn associated with extensions of the energy operator in a Pontryagin space in THEORETICAL AND MATHEMATICAL PHYSICS
  • 1997-09. On rank one perturbations of selfadjoint operators in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • 2004. Singular Perturbations as Range Perturbations in a Pontryagin Space in SPECTRAL METHODS FOR OPERATORS OF MATHEMATICAL PHYSICS
  • 1999-12. On generalized resolvents of Hermitian relations in Krein spaces in JOURNAL OF MATHEMATICAL SCIENCES
  • 2003-04. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ mathcal{H} $\end{document}-n-perturbations of Self-adjoint Operators and Krein's Resolvent Formula in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • 1998. The sum of matrix nevanlinna functions and self-adjoint extensions in exit spaces in RECENT PROGRESS IN OPERATOR THEORY
  • 2000. Self-adjoint Operators with Inner Singularities and Pontryagin Spaces in OPERATOR THEORY AND RELATED TOPICS
  • 1987-05. New analytically solvable models of relativistic point interactions in LETTERS IN MATHEMATICAL PHYSICS
  • 2000. Singular Operator as a Parameter of Self-adjoint Extensions in OPERATOR THEORY AND RELATED TOPICS
  • 1995-01. The extension theory of Hermitian operators and the moment problem in JOURNAL OF MATHEMATICAL SCIENCES
  • 1992-12. On a formula of the generalized resolvents of a nondensely defined Hermitian operator in UKRAINIAN MATHEMATICAL JOURNAL
  • 1994-02. Relativistic point interaction in LETTERS IN MATHEMATICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1023/b:mpag.0000007189.09453.fc

    DOI

    http://dx.doi.org/10.1023/b:mpag.0000007189.09453.fc

    DIMENSIONS

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