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Normal modes for Green's functions and the method of theta functions

Published online by Cambridge University Press:  24 October 2008

Riho Terras
Riho Terras
Affiliation:
University of California, La Jolla, California
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Abstract

The eigenfunctions for four types of bounded plane domains are constructed by a group-theoretic method. The group theory is then used to prove a completeness theorem and to derive a theta function transformation formula. Rapidly convergent series for the Green's functions of the Laplace operator on these domains are then constructed. Final formulas are summarized without reference to group theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 2 , March 1981 , pp. 331 - 341
Copyright
Copyright © Cambridge Philosophical Society 1981

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