IJPAM: Volume 89, No. 3 (2013)

DISCRETENESS CRITERION FOR THE SPECTRUM OF
THE SCHRÖDINGER OPERATOR ON WEIGHTED
QUASIMODEL MANIFOLDS

Andrey Svetlov
Mathematics and IT Department
Volgograd State University
pr. Universitetskiy, 100, Volgograd, 400062, RUSSIA


Abstract. In this paper we study the spectrum of the Schrödinger operator on the weighted quasimodel manifolds. We obtain the discreteness criterion for this problem with some restrictions on the potential and geometry of the manifold.

Received: August 31, 2013

AMS Subject Classification: 58J50

Key Words and Phrases: noncompact Riemannian manifold, quasimodel manifold, Schrödinger operator, discrete spectrum

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DOI: 10.12732/ijpam.v89i3.10 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 3