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Spectral Enclosures for Non-self-adjoint Discrete Schrödinger Operators

  • Orif O. IbrogimovEmail author
  • František Štampach
Article
  • 34 Downloads

Abstract

We study location of eigenvalues of one-dimensional discrete Schrödinger operators with complex \(\ell ^{p}\)-potentials for \(1\le p\le \infty \). In the case of \(\ell ^{1}\)-potentials, the derived bound is shown to be optimal. For \(p>1\), two different spectral bounds are obtained. The method relies on the Birman–Schwinger principle and various techniques for estimations of the norm of the Birman–Schwinger operator.

Keywords

Discrete Schrödinger operator Birman–Schwinger principle Point spectrum Jacobi matrix 

Mathematics Subject Classification

34L15 47B36 47A75 

Notes

Acknowledgements

The first author thanks Prof. David Krejčiřík for stimulating discussions. The second author acknowledges financial support by the Ministry of Education, Youth and Sports of the Czech Republic Project No. CZ.02.1.01/0.0/0.0/16_019/0000778.

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Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PraguePraha 2Czech Republic
  2. 2.Department of Applied Mathematics, Faculty of Information TechnologyCzech Technical University in PraguePrahaCzech Republic

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