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Full- and partial-range eigenfunction expansions for Sturm-Liouville problems with indefinite weights*

Published online by Cambridge University Press:  14 November 2011

Hans G. Kaper ,
Man Kam Kwong ,
C. G. Lekkerkerker  and
A. Zettl
Hans G. Kaper
Affiliation:
Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, U.S.A.
Man Kam Kwong
Affiliation:
Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, U.S.A.
C. G. Lekkerkerker
Affiliation:
Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, U.S.A.
A. Zettl
Affiliation:
Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, U.S.A.
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Synopsis

This article is concerned with eigenvalue problems of the form Au = λTu in a Hilbert space H, where Ais a selfadjoint positive operator generated by a second-order Sturm-Liouville differential expression and T a selfadjoint indefinite multiplicative operator which is one-to-one. Emphasis is on the full-range and partial-range expansionproperties of the eigenfunctions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 98 , Issue 1-2 , 1984 , pp. 69 - 88
Copyright
Copyright © Royal Society of Edinburgh 1984

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