Heisenberg uncertainty principle for a fractional power of the Dunkl transform on the real line

DOI10.1016/J.CAM.2015.06.013zbMath1331.42007arXiv1311.2295OpenAlexW2204166758MaRDI QIDQ893121

Fethi Bouzeffour, Sami Ghazouani

Publication date: 13 November 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.2295

zbMATH Keywords

generalized Hermite polynomialsfractional Fourier transformHeisenberg uncertainty principleDunkl transformgeneralized Sobolev spaces

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Related Items (13)

Quantitative uncertainty principles associated with the \(k\)-generalized Stockwell transform ⋮ Novel uncertainty principles for two-sided quaternion linear canonical transform ⋮ New uncertainty principles for the $(k,a)$-generalized wavelet transform ⋮ Canonical Fourier-Bessel transform and their applications ⋮ Hardy type theorems for linear canonical Dunkl transform ⋮ Generalized translation operator and uncertainty principles associated with the deformed Stockwell transform ⋮ Time-frequency localization for the fractional Fourier transform in signal processing and uncertainty principles ⋮ Algebraic approach to the Dunkl-Coulomb problem and Dunkl oscillator in arbitrary dimensions ⋮ A unified class of integral transforms related to the Dunkl transform ⋮ Harmonic analysis associated to the canonical Fourier Bessel transform ⋮ Dunkl-Stockwell transform and its applications to the time-frequency analysis ⋮ Fractional Jacobi-Dunkl transform: properties and application ⋮ Coherent states of the one-dimensional Dunkl oscillator for real and complex variables and the Segal–Bargmann transformation of Dunkl-type

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• Integral Kernels with Reflection Group Invariance
• An uncertainty principle for Hankel transforms
• A Fractional Power for Dunkl Transforms in $ L^{2}(\R^{N}, \omega_{k}(x)dx)$
• Uncertainty Inequalities for Hankel Transforms

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