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Spectral gaps of Schroedinger operators on hyperbolic space

Karp, L.; Peyerimhoff, N.


L. Karp


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.


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
Publisher Wiley-VCH Verlag
Peer Reviewed Peer Reviewed
Volume 217
Pages 105-124