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The Sampling Theorem, DIRICHLET Series and BESSEL Functions
Author(s) -
Klusch Dieter
Publication year - 1991
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19911540111
Subject(s) - mathematics , analytic number theory , bessel function , dirichlet series , riemann zeta function , dirichlet distribution , divergent series , series (stratigraphy) , mathematical analysis , riemann hypothesis , dirichlet l function , pure mathematics , summation by parts , paleontology , biology , boundary value problem
Abstract Generalized forms of the classical WHITTAKER‐KOTELNIKOV‐SHANNON sampling theorem and of the extended BUTZER‐SPLETTSTÖSSER‐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 SCHLÖMILCH series is established.