Spectral gaps of Schroedinger operators on hyperbolic space

Karp, L.; Peyerimhoff, N.

Abstract

This paper is mainly concerned with estimates of spectral gaps of Schroedinger operators with smooth potential on real hyperbolic space. The estimates are obtained by explicit constructions of approximate generalized eigenfunctions. Among the results are analogues of classical uniform and asymptotic gap estimates for periodic Schroedinger operators in the Euclidean space. Moreover, in the more general setting of an arbitrary complete non-compact Riemannian manifold, we derive a growth condition for a generalized eigenfunction such that the corresponding eigenvalue lies in the spectrum of the Schroedinger operator.

Citation

Karp, L., & Peyerimhoff, N. (2000). Spectral gaps of Schroedinger operators on hyperbolic space. Mathematische Nachrichten, 217, 105-124

• Journal Article Type: Article
• Publication Date: 2000
• Journal: Mathematische Nachrichten
• Print ISSN: 0025-584X
• Electronic ISSN: 1522-2616
• Publisher: Wiley-VCH Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 217
• Pages: 105-124
• Public URL: https://durham-repository.worktribe.com/output/1577383