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Construction of regular and singular Green's functions

Published online by Cambridge University Press:  30 January 2012

Aiping Wang ,
Jerry Ridenhour  and
Anton Zettl
Aiping Wang
Affiliation:
Mathematics Department, Tianjin University of Science and Technology, Tianjin 300457, People's Republic of China (aiping@tust.edu.cn)
Jerry Ridenhour
Affiliation:
Mathematics Department, University of Northern Iowa, 50614 Cedar Falls, IA 50614, USA (jerry.ridenhour@uni.edu)
Anton Zettl
Affiliation:
Mathematics Department, Northern Illinois University, DeKalb, IL 60115, USA (zettl@math.niu.edu)
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Abstract

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The Green function of singular limit-circle problems is constructed directly for the problem, not as a limit of sequences of regular Green's functions. This construction is used to obtain adjointness and self-adjointness conditions which are entirely analogous to the regular case. As an application, a new and explicit formula for the Green function of the classical Legendre problem is found.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 1 , February 2012 , pp. 171 - 198
Copyright
Copyright © Royal Society of Edinburgh 2012