Letters in Mathematical Physics

, Volume 106, Issue 11, pp 1465–1478 | Cite as

On the Number of Discrete Eigenvalues of a Discrete Schrödinger Operator with a Finitely Supported Potential

  • Yusuke Hayashi
  • Yusuke Higuchi
  • Yuji Nomura
  • Osamu Ogurisu
Article
  • 86 Downloads

Abstract

On the d-dimensional lattice \({\mathbb{Z}^d}\) and the r-regular tree \({T^r}\), an exact expression for the number of discrete eigenvalues of a discrete Laplacian with a finitely supported potential is described in terms of the support and the intensities of the potential on each case. In particular, the number of eigenvalues less than the infimum of the essential spectrum is bounded by the number of negative intensities.

Keywords

discrete Schrödinger operator discrete eigenvalue finitely supported potential finite-rank perturbation Green function 

Mathematics Subject Classification

39A12 47A75 34L40 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Yusuke Hayashi
    • 1
  • Yusuke Higuchi
    • 2
  • Yuji Nomura
    • 3
  • Osamu Ogurisu
    • 1
  1. 1.Division of Mathematical and Physical SciencesKanazawa UniversityKanazawaJapan
  2. 2.College of Arts and SciencesShowa UniversityFujiyoshidaJapan
  3. 3.Graduate School of Material ScienceUniversity of HyogoHimejiJapan

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