The sampling theorem, Dirichlet series and Hankel transforms

DOI10.1016/0377-0427(92)90001-EzbMath0768.94004MaRDI QIDQ1208559

Dieter Klusch

Publication date: 16 May 1993

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Hankel transformDirichlet seriesRiemann's zeta functiontheta-functionsignal analysisapproximate sampling theoremBrown-Butzer-Splettstößer approximate sampling expansionNielsen- Doetsch summation formula for Bessel functionsperiodic Hilbert kernelWhittaker-Kotelnikov- Shannon sampling theoremWhittaker's cardinal series

Mathematics Subject Classification ID

Inclusion and equivalence theorems in summability theory (40D25) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items (4)

On the Hankel transformation of order zero ⋮ One approach to some general integral transforms and its applications ⋮ Mellin transforms and asymptotics: Harmonic sums ⋮ Seven pivotal theorems of Fourier analysis, signal analysis, numerical analysis and number theory: their interconnections

Cites Work

• Aspects of de La Vallée Poussin's work in approximation and its influence
• On Riemann's functional equation
• On Riemann's functional equations
• Hecke's functional equation and arithmetical identities
• The Euler-MacLaurin summation formula, the sampling theorem, and approximate integration over the real axis
• The sampling theorem and linear prediction in signal analysis
• On the summation of Bessel functions and Hankel transforms
• Functional equations with multiple gamma factors and the average order of arithmetical functions
• Some properties of modular relations
• Sur l'équation fonctionnelle de Riemann et la formule sommatoire de Poisson
• Five short stories about the cardinal series
• The Sampling Theorem, DIRICHLET Series and BESSEL Functions
• Identities Involving the Coefficients of a Class of Dirichlet Series. I
• Dirichlet series with functional equations and related arithmetical identities
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