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An expansion theory for non-self-adjoint boundary-value problems

Published online by Cambridge University Press:  14 November 2011

Philip W. Walker
Philip W. Walker
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77004, U.S.A.
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Synopsis

This paper deals with two-point boundary-value problems for ordinary differential equations and the operators which they induce in the appropriate Hilbert space. The problems arenot required to be self-adjoint. No auxiliary condition such as Birkhoff-regularity is imposed. If T is such an operator, it may well have no meaningful spectral structure. It is shown, however, that when T is composed with its adjoint, the result is a non-negative self-adjoint differential operator. The eigenvalues and eigenfunctions of this composite operator are used to delineate the domain, action, range, and generalised inverse of T.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 108 , Issue 1-2 , 1988 , pp. 11 - 26
Copyright
Copyright © Royal Society of Edinburgh 1988

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