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Eigenvalues of periodic Sturm-Liouville problems by the Shannon-Whittaker sampling theorem

Author: Amin Boumenir
Journal: Math. Comp. 68 (1999), 1057-1066
MSC (1991): Primary 34L15, 42A15
Published electronically: February 10, 1999
MathSciNet review: 1627850
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Abstract: We are concerned with the computation of eigenvalues of a periodic Sturm-Liouville problem using interpolation techniques in Paley-Wiener spaces. We shall approximate the Hill discriminant by sampling a few of its values and then find its zeroes which are the square roots of the eigenvalues. Computable error estimates are provided together with eigenvalue enclosures.

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Additional Information

Amin Boumenir
Affiliation: Department of Mathematics, College of Sciences, Sultan Qaboos University, P.O. Box 36, Alkhod 123, Muscat, Sultanate of Oman

Keywords: Periodic Sturm-Liouville problems, eigenvalue problem, interpolation, Shannon-Whittaker sampling theorem
Received by editor(s): June 9, 1997
Received by editor(s) in revised form: October 28, 1997
Published electronically: February 10, 1999
Article copyright: © Copyright 1999 American Mathematical Society