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Darboux transformations and the factorization of generalized Sturm–Liouville problems

Published online by Cambridge University Press:  04 February 2010

Paul A. Binding ,
Patrick J. Browne  and
Bruce A. Watson
Paul A. Binding
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada, ([email protected])
Patrick J. Browne
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E6, Canada, ([email protected])
Bruce A. Watson
Affiliation:
School of Mathematics, University of the Witwatersrand, Private Bag 3, PO WITS 2050, South Africa, ([email protected])
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Abstract

A version of the Darboux transformation is explored for Sturm-Liouville problems with eigenvalue-dependent boundary conditions, from differential-equation and operator-theoretic viewpoints. Some of the literature on Darboux's transformation is related in a historical introduction.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 1 , February 2010 , pp. 1 - 29
Copyright
Copyright © Royal Society of Edinburgh 2010

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