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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
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77004, U.S.A.

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
Copyright
Copyright © Royal Society of Edinburgh 1988

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