A unified class of integral transforms related to the Dunkl transform

DOI10.1016/j.jmaa.2016.12.054zbMath1359.44002OpenAlexW2563964910MaRDI QIDQ509026

El Amine Soltani, Sami Ghazouani, Ahmed Fitouhi

Publication date: 8 February 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.12.054

zbMATH Keywords

integral transformsPlancherel formulaquantum harmonic oscillatorcanonical commutation relationsemigroups of operatorslinear canonical transformRiemann-Lebesgue lemmaDunkl transformBochner-type identitycanonical Hankel transformfractional Dunkl transformFresnel transformgeneralized Hermite polynomials and functions

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05)

Related Items (12)

Windowed linear canonical transform and its applications to the time-frequency analysis ⋮ Linear canonical deformed Hankel transform and the associated uncertainty principles ⋮ The Fourier transform associated to the \(k\)-hyperbolic Dirac operator ⋮ Canonical Fourier-Bessel transform and their applications ⋮ Hardy type theorems for linear canonical Dunkl transform ⋮ Linear canonical Fourier–Bessel wavelet transform: properties and inequalities ⋮ Prolate spheroidal wave functions associated with the canonical Fourier–Bessel transform and uncertainty principles ⋮ Algebraic approach to the Dunkl-Coulomb problem and Dunkl oscillator in arbitrary dimensions ⋮ Harmonic analysis associated to the canonical Fourier Bessel transform ⋮ A variation on uncertainty principles for quaternion linear canonical transform ⋮ Quantitative uncertainty principles for the canonical Fourier-Bessel transform ⋮ 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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