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ON THE RESOLVENT OF THE LAPLACE–BELTRAMI OPERATOR IN HYPERBOLIC SPACE

Part of: Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  24 April 2015

GUSEIN SH. GUSEINOV
GUSEIN SH. GUSEINOV*
Affiliation:
Department of Mathematics, Atilim University, 06836 Incek, Ankara, Turkey email huseyin.huseyin@atilim.edu.tr
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Abstract

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In this paper, a detailed description of the resolvent of the Laplace–Beltrami operator in $n$-dimensional hyperbolic space is given. The resolvent is an integral operator with the kernel (Green’s function) being a solution of a hypergeometric differential equation. Asymptotic analysis of the solution of this equation is carried out.

Keywords

hyperbolic spaceLaplace–Beltrami operatorGreen’s functionresolvent

MSC classification

Secondary: 35P05: General topics in linear spectral theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 2 , October 2015 , pp. 186 - 206
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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