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Spectral properties of Schrödinger operators on radial N-dimensional infinite trees

  • Yehuda PinchoverEmail author
  • Gershon Wolansky
  • Daphne Zelig
Article
  • 93 Downloads

Abstract

We study the discreteness of the spectrum of Schrödinger operators which are defined on a class of radial N-dimensional rooted trees of a finite or infinite volume, and are subject to a certain mixed boundary condition. We present a method to estimate their eigenvalues using operators on a one-dimensional tree. These operators are called width-weighted operators, since their coefficients depend on the section width or area of the N-dimensional tree. We show that the spectrum of the width-weighted operator tends to the spectrum of a one-dimensional limit operator as the sections width tends to zero. Moreover, the projections to the one-dimensional tree of eigenfunctions of the N-dimensional Laplace operator converge to the corresponding eigenfunctions of the one-dimensional limit operator.

Keywords

Weight Function Laplace Operator Discrete Spectrum Lipschitz Domain Counting Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Hebrew University of Jerusalem 2008

Authors and Affiliations

  • Yehuda Pinchover
    • 1
    Email author
  • Gershon Wolansky
    • 1
  • Daphne Zelig
    • 1
  1. 1.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

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