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The Sampling Theorem, DIRICHLET Series and BESSEL Functions

✍ Scribed by Dieter Klusch

Publisher
John Wiley and Sons
Year
1991
Tongue
English
Weight
387 KB
Volume
154
Category
Article
ISSN
0025-584X

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✦ Synopsis

Generalized forms of the classical WHITTAKER-KOTELNIKOV-SHANNON sampling theorem and of the extended BUTZER-SPLETTST~SSER-STENS sampling expansion for nonbandlimited signal functions are deduced from the famous functional equation of RIEMANN'S zeta-function and from the well known NIELSEN-DOETSCH summation formula for BESSEL functions. Hence a rather surprising connection between fundamental theorems of signal analysis and the theories of DIRICHLET and SCHLOMILCH series is established.

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## Abstract Let \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$K/\mathbb {Q}$\end{document} be a finite Galois extension with the Galois group __G__, and let Ο‡ be a character of __G__ with the associated Artin __L__‐function __L__(__s__, Ο‡) defined in β„œ(__s__) > 1 by t