The classical and approximate sampling theorems and their equivalence for entire functions of exponential type

DOI10.1016/j.jat.2013.11.010zbMath1370.42002OpenAlexW2068651471MaRDI QIDQ2636663

Rudolf L. Stens, Paul L. Butzer, Gerhard Schmeisser

Publication date: 30 January 2014

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2013.11.010

zbMATH Keywords

Paley-Wiener theoremsampling theorembandlimited signalsfunctions of exponential typenon-bandlimited signals

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Sampling theory in information and communication theory (94A20)

Related Items (10)

On the Paley-Wiener theorem in the Mellin transform setting ⋮ Nonuniform sampling and approximation in Sobolev space from perturbation of the framelet system ⋮ Askey–Wilson operator on entire functions of exponential type ⋮ Oversampling and aliasing in de Branges spaces arising from Bessel operators ⋮ Periodic Bézier curves ⋮ Sampling and Average Sampling in Quasi Shift-Invariant Spaces ⋮ A fresh approach to classical Eisenstein series and the newer Hilbert–Eisenstein series ⋮ Seven pivotal theorems of Fourier analysis, signal analysis, numerical analysis and number theory: their interconnections ⋮ The Mellin–Parseval formula and its interconnections with the exponential sampling theorem of optical physics ⋮ On the approximate form of Kluvánek's theorem

Cites Work

• Shannon's sampling theorem for bandlimited signals and their Hilbert transform, Boas-type formulae for higher order derivatives -- the aliasing error involved by their extensions from bandlimited to non-bandlimited signals
• The summation formulae of Euler-Maclaurin, Abel-Plana, Poisson, and their interconnections with the approximate sampling formula of signal analysis
• Numerical differentiation inspired by a formula of R.P. Boas
• The sampling theorem and linear prediction in signal analysis
• Classical and approximate sampling theorems; studies in the \(L^{p}(\mathbb R)\) and the uniform norm
• The sampling theorem, Poisson's summation formula, general Parseval formula, reproducing kernel formula and the Paley–Wiener theorem for bandlimited signals – their interconnections
• A Quadrature Formula for Entire Functions of Exponential Type
• Quadrature Formulae and Functions of Exponential Type
• On Bernstein's Inequality and the Norm of Hermitian Operators
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