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Expansion theorems for Birkhoff-regular differential-boundary operators

Published online by Cambridge University Press:  14 November 2011

Manfred Möller
Manfred Möller
Affiliation:
Naturwissenschaftliche Fakultät I-Mathematik, Universität Regensburg, Universitätsstraße 31, 8400 Regensburg, Germany
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Synopsis

In this paper we consider differential-boundary operators T over a finite interval depending on a complex parameter. A differential-boundary operator admits boundary conditions in the differential part. The boundary part contains multipoint boundary conditions and integral conditions. For Birkhoff-regular boundary conditions we prove that every Lp -function is expansible into a series with respect to the eigenfunctions and the associated functions of the differential-boundary operator. Here the Birkhoff-regularity only depends on the boundary conditions at the endpoints of the interval, i.e. T is Birkhoff-regular if and only if T0 is Birkhoff-regular where T0 arises from T by omitting the boundary part in the differential equations, the interior point boundary conditions and the integral condition.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 3-4 , 1987 , pp. 349 - 374
Copyright
Copyright © Royal Society of Edinburgh 1987

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