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VOL. 34 | 2002 Behavior of Eigenfunctions near the Ideal Boundary of Hyperbolic Space
Harold Donnelly

Editor(s) Kenji Fukaya, Seiki Nishikawa, Joel Spruck

Abstract

The spectrum of the Laplacian on hyperbolic space is a proper subset of the positive reals. We study eigenfunctions, defined on the complements of compact sets, whose eigenvalues lie below the bottom of the spectrum. Such eigenfunctions may arise by perturbing the metric on compact subsets of the space. One divides the eigenfunctions by normalizing factors, so that the quotients have analytic boundary values on the ideal boundary at infinity. The renormalized eigenfunctions are approximated by special polynomials, in nontangential approach regions to the ideal boundary.

Information

Published: 1 January 2002
First available in Project Euclid: 31 December 2018

zbMATH: 1035.58019
MathSciNet: MR1925733

Digital Object Identifier: 10.2969/aspm/03410015

Subjects:
Primary: 58G25

Rights: Copyright © 2002 Mathematical Society of Japan

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