The uncertainty principle lemma under gravity and the discrete spectrum of Schrödinger operators

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

The uncertainty principle lemma for the Laplacian on Euclidean spaces shows the borderline-behavior of a potential for the following question : whether the Schrödinger operator has a finite or infinite number of the discrete pectrum. In this paper, we will give a generalization of this lemma on Euclidean spaces to that on large classes of complete noncompact manifolds. Replacing Euclidean spaces by some specific classes of complete noncompact manifolds, including hyperbolic spaces, we also establish some criterions for the above-type question.
19 pages, 1 figure

Keywords

Differential Geometry, Spectral Theory, 58J50, 35J10

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/215476

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0812.4663
 http://arxiv.org/abs/0812.4663

Collections

arXiv