The multiplier of the interval [−1, 1] for the Dunkl transform of arbitrary order on the real line

DOI10.1080/10652469.2015.1038707zbMath1318.42005OpenAlexW2209388764MaRDI QIDQ5262286

Luz Roncal, Óscar Ciaurri, Juan Luis Varona

Publication date: 13 July 2015

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2015.1038707

zbMATH Keywords

multipliersBessel functionsDunkl transform

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Multipliers in one variable harmonic analysis (42A45)

Related Items

Boole-Dunkl polynomials and generalizations, Discrete Appell-Dunkl sequences and Bernoulli-Dunkl polynomials of the second kind

Cites Work

• Interpolation by weighted Paley-Wiener spaces associated with the Dunkl transform
• Bilinear biorthogonal expansions and the Dunkl kernel on the real line
• Riesz transform and Riesz potentials for Dunkl transform
• The multiplier of the interval \([-1,1\) for the Dunkl transform on the real line]
• A transference theorem for the Dunkl transform and its applications
• The Dunkl transform
• Uncertainty principles involvingL¹-norms for the Dunkl transform
• Generalization of the Bochner identity for the Dunkl transform
• Dunkl transforms and Dunkl convolutions on functions and distributions with restricted growth
• Integral Kernels with Reflection Group Invariance
• Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators
• A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Dunkl transform