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MULTIVARIATE SAMPLING THEOREMS ASSOCIATED WITH MULTIPARAMETER DIFFERENTIAL OPERATORS

Published online by Cambridge University Press:  23 May 2005

M. H. Annaby
M. H. Annaby
Affiliation:
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt (mhannaby@yahoo.com)
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Abstract

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We investigate the multivariate sampling theory associated with multiparameter eigenvalue problems. A several-variable counterpart of the classical sampling theorem of Whittaker, Kotel’nikov and Shannon is given. It arose when the multiparameter system has order one. Two-dimensional sampling theorems associated with two-parameter systems of second-order differential operators will be established. The sampling formulae are of multivariate non-uniform Lagrange interpolation type. Unlike many of the known formulae, the interpolating functions are not necessarily products of single variable functions.

Keywords

Primary 32A1534B0894A20multiparameter eigenvalue problemssampling theoryLagrange interpolations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 48 , Issue 2 , June 2005 , pp. 257 - 277
Copyright
Copyright © Edinburgh Mathematical Society 2005