A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Dunkl transform

DOI10.1090/S0002-9939-07-08831-4zbMath1278.94036OpenAlexW2052611669MaRDI QIDQ5291941

Óscar Ciaurri, Juan Luis Varona

Publication date: 19 June 2007

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-07-08831-4

zbMATH Keywords

reproducing kernelBessel functionsorthonormal systemDunkl transformWSK sampling theorem

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Sampling theory in information and communication theory (94A20)

Related Items (16)

The spectrum of the right inverse of the Dunkl operator ⋮ Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions ⋮ Interpolation by weighted Paley-Wiener spaces associated with the Dunkl transform ⋮ Equivalence of \(K\)-functionals and modulus of smoothness generated by a Dunkl type operator on the interval \((-1, 1)\) ⋮ Boundedness and compactness of Dunkl two-wavelet multipliers ⋮ Some problems of approximation theory in the spaces \(L_p\) on the line with power weight ⋮ Generalization of the Dunkl operator on the space of entire functions ⋮ A Paley-Wiener theorem for the Askey-Wilson function transform ⋮ Mean convergence of Fourier-Dunkl series ⋮ Fourier-Dunkl system of the second kind and Euler-Dunkl polynomials ⋮ Bilinear biorthogonal expansions and the Dunkl kernel on the real line ⋮ Bernoulli-Dunkl and Euler-Dunkl polynomials and their generalizations ⋮ Asymptotic behavior of Bernoulli-Dunkl and Euler-Dunkl polynomials and their zeros ⋮ An uncertainty inequality for Fourier-Dunkl series ⋮ On the Dunkl convolution equations in spaces of type ⋮ The multiplier of the interval [−1, 1 for the Dunkl transform of arbitrary order on the real line]

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• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• A 𝑞-analogue of the Whittaker-Shannon-Kotel’nikov sampling theorem
• Orthogonal Sampling Formulas: A Unified Approach
• An Interpolation Series Associated with the Bessel-Hankel Transform

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