Eigenvalue asymptotics for the Schrödinger operators on the real and the complex hyperbolic spaces

Yuzuru Inahama, Shin Ichi Shirai

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Abstract

We study the large eigenvalue asymptotics for the Schrödinger operator HV=-1/2Δ+V on the real and the complex hyperbolic n-spaces. Here Δ is the Laplace-Beltrami operator and V is a scalar potential. We assume that V is real-valued, continuous, semi-bounded from below and diverges at infinity in an appropriate sense. Then it is proven that the number of eigenvalues of HV less than λ behaves semi-classically as λ↗∞. This is a natural generalization of the result obtained by Inahama and Shirai [Eigenvalue asymptotics for the Schrödinger operators on the hyperbolic plane, J. Funct. Anal., submitted for publication].

Original languageEnglish
Pages (from-to)589-627
Number of pages39
JournalJournal des Mathematiques Pures et Appliquees
Volume83
Issue number5
DOIs
Publication statusPublished - May 1 2004
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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