A Generalized Sampling Theorem for Locally Compact Abelian Groups

DOI10.2307/2153577zbMath0808.65144OpenAlexW2125494265MaRDI QIDQ4305965

Adel Faridani

Publication date: 16 March 1995

Full work available at URL: https://doi.org/10.2307/2153577

zbMATH Keywords

Fourier transformsampling theoremlattice rulesinverse transformlocally compact abelian groupmultidimensional quadrature

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items

Geometric aspects of frame representations of abelian groups ⋮ An \(L^2\)-stability estimate for periodic nonuniform sampling in higher dimensions ⋮ Finding duality for Riesz bases of exponentials on multi-tiles ⋮ Density theorems for nonuniform sampling of bandlimited functions using derivatives or bunched measurements ⋮ Exponential bases for partitions of intervals ⋮ Sampling Theory in a Fourier Algebra Setting ⋮ Seven pivotal theorems of Fourier analysis, signal analysis, numerical analysis and number theory: their interconnections ⋮ Recovery of Band-Limited Functions on Locally Compact Abelian Groups from Irregular Samples ⋮ Gaussian regularized periodic nonuniform sampling series ⋮ On Regular Generalized Sampling in T-Invariant Subspaces of a Hilbert Space: An Overview ⋮ On the approximate form of Kluvánek's theorem ⋮ Sampling associated with a unitary representation of a semi-direct product of groups: a filter bank approach

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