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Eigenvalues of Non-selfadjoint Operators: A Comparison of Two Approaches

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Mathematical Physics, Spectral Theory and Stochastic Analysis

Part of the book series: Operator Theory: Advances and Applications ((APDE,volume 232))

Abstract

The central problem we consider is the distribution of eigenvalues of closed linear operators which are not selfadjoint, with a focus on those operators which are obtained as perturbations of selfadjoint linear operators. Two methods are explained and elaborated. One approach uses complex analysis to study a holomorphic function whose zeros can be identified with the eigenvalues of the linear operator. The second method is an operator theoretic approach involvingthe numerical range. General results obtained by the two methods are derived and compared. Applications to non-selfadjoint Jacobi and Schrödinger operators are considered. Some possible directions for future research are discussed.

Mathematics Subject Classification (2010). 47A10, 47A75, 47B36, 81Q12.

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Author information

Authors and Affiliations

  1. Institute for Mathematics, Clausthal University of Technology, Clausthal, Germany

    Michael Demuth

  2. Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany

    Marcel Hansmann

  3. Department of Mathematics, Braude College, Karmiel, Israel

    Guy Katriel

Authors
  1. Michael Demuth
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  2. Marcel Hansmann
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  3. Guy Katriel
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Correspondence to Michael Demuth .

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Editors and Affiliations

  1. Institut für Mathematik, TU Clausthal, Clausthal-Zellerfeld, Germany

    Michael Demuth

  2. Fakultät für Mathematik und Informatik, FernUniversität Hagen, Hagen, Germany

    Werner Kirsch

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Demuth, M., Hansmann, M., Katriel, G. (2013). Eigenvalues of Non-selfadjoint Operators: A Comparison of Two Approaches. In: Demuth, M., Kirsch, W. (eds) Mathematical Physics, Spectral Theory and Stochastic Analysis. Operator Theory: Advances and Applications(), vol 232. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0591-9_2

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