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multiparameter eigenvalue problems

Proceedings of the Edinburgh Mathematical Society (1)

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MULTIVARIATE SAMPLING THEOREMS ASSOCIATED WITH MULTIPARAMETER DIFFERENTIAL OPERATORS
M. H. Annaby
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 48 / Issue 2 / June 2005

Published online by Cambridge University Press:

23 May 2005, pp. 257-277
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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.