A note on Whittaker's cardinal series in harmonic analysis

DOI10.1017/S001309150001779XzbMath0616.43006OpenAlexW1982852131MaRDI QIDQ4725114

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Publication date: 1986

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s001309150001779x

zbMATH Keywords

stochastic processesPaley-Wiener theoremsampling theoremParseval's theoremcardinal seriesHeisenberg nilmanifoldabelian locally compact topological groupdisjoint translatesmeasurable subset of dual groupspectral set of \(L^ 2(G)\)

Mathematics Subject Classification ID

Filtering in stochastic control theory (93E11) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items (4)

Sampling and aliasing for functions band-limited to a thin shell ⋮ Approximating signals in the abstract ⋮ Shannon's sampling theorem, incongruent residue classes and Plancherel's theorem ⋮ On the approximate form of Kluvánek's theorem

Cites Work

• A Sampling Theorem for Stationary (Wide Sense) Stochastic Processes
• Five short stories about the cardinal series
• The Shannon sampling theorem—Its various extensions and applications: A tutorial review
• Sampling Theorems for Nonstationary Random Processes
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