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Pointwise convergence of eigenfunction expansions, associated with a pair of ordinary differential expressions

Published online by Cambridge University Press:  14 November 2011

Earl A. Coddington ,
Aalt Dijksma  and
Hendrik S. V. de Snoo
Earl A. Coddington
Affiliation:
Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90024, U.S.A.
Aalt Dijksma
Affiliation:
Mathematisch Instituut, Rijksuniversiteit, Groningen, The Netherlands
Hendrik S. V. de Snoo
Affiliation:
Mathematisch Instituut, Rijksuniversiteit, Groningen, The Netherlands
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Synopsis

For the differential equation Lf = λMf on an open interval of ℝ, a theory in terms of relations in a Hilbert space associated with M was developed in a paper by Coddington and de Snoo, and eigenfunction expansions were derived in a paper by Dijksma and de Snoo. In the case of a regular problem on a compact interval, pointwise convergence of the expansions was shown in another paper by Coddington and de Snoo. Here, we show pointwise convergence in the general singular case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 59 - 71
Copyright
Copyright © Royal Society of Edinburgh 1984

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