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One and multidimensional sampling theorems associated with Dirichlet problems

✍ Scribed by Mahmoud H. Annaby

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
249 KB
Volume
21
Category
Article
ISSN
0170-4214

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✦ Synopsis

We use the eigenfunction expansion of Green's function of Dirichlet problems to obtain sampling theorems. The analytic properties of the sampled integral transforms as well as the uniform convergence of the sampling series are proved without any restrictions on the integral transforms. We obtain a one-and multi-dimensional versions of sampling theorems. In both cases the sampling series are written in terms of Lagrange-type interpolation expansions. Some examples and the truncation error as well as the stability of the obtained sampling expansions are discussed at the end of the paper.

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## Abstract We study the asymptotic behaviour of the solution __u__~__n__~ of a linear elliptic equation posed in a fixed domain Ξ©. The solution __u__~__n__~ is assumed to satisfy a Dirichlet boundary condition on Ξ“~__n__~, where Ξ“~__n__~ is an arbitrary sequence of subsets of βˆ‚Ξ©, and a Neumman bou