Abstract

The Sampling Method A Boumenir We shall explain how the Shannon sampling theorem is used for the computation of eigenvalues of Sturm-Liouville problems. In this talk we shall see the connection between the Gelfand-Levitan theory and the approximation in Paley-Wiener spaces for regular Strum-Liouville problem. Computable error bounds for the approximated eigenvalues will be derived from the truncation error in the Shannon sampling theorem in a very simple way. Singular problems will also be discussed.

General Enquiries Dr. Malcolm Brown. Computer Science Cardiff University PO Box 916 Cardiff CF24 3XF, U.K. Malcom@cs.cf.ac.uk

N.B. All Mathematics appears in TeX/LaTeX source.

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