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One and multidimensional sampling theorems associated with Dirichlet problems
Author(s) -
Annaby Mahmoud H.
Publication year - 1998
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19980310)21:4<361::aid-mma954>3.0.co;2-e
Subject(s) - mathematics , sampling (signal processing) , eigenfunction , interpolation (computer graphics) , dirichlet distribution , dirichlet series , convergence (economics) , truncation error , stability (learning theory) , series (stratigraphy) , truncation (statistics) , lagrange polynomial , mathematical analysis , calculus (dental) , statistics , boundary value problem , computer graphics (images) , dentistry , filter (signal processing) , economic growth , biology , paleontology , quantum mechanics , machine learning , computer vision , animation , medicine , eigenvalues and eigenvectors , physics , economics , polynomial , computer science
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. © 1998 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.