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

Yuzuru Inahama, Shin Ichi Shirai

Research output: Contribution to journalArticle

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

Fingerprint

Eigenvalue Asymptotics
Complex Hyperbolic Space
Hyperbolic Plane
Laplace-Beltrami Operator
Largest Eigenvalue
Operator
Diverge
Infinity
Scalar
Eigenvalue
Generalization

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Eigenvalue asymptotics for the Schrödinger operators on the real and the complex hyperbolic spaces. / Inahama, Yuzuru; Shirai, Shin Ichi.

In: Journal des Mathematiques Pures et Appliquees, Vol. 83, No. 5, 01.05.2004, p. 589-627.

Research output: Contribution to journalArticle

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