Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-30T13:05:26.878Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected])
Jerry Ridenhour
Affiliation:
Mathematics Department, University of Northern Iowa, 50614 Cedar Falls, IA 50614, USA ([email protected])
Anton Zettl
Affiliation:
Mathematics Department, Northern Illinois University, DeKalb, IL 60115, USA ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)