Practical inversion formulas for the Dunkl–Gabor transform on ℝd

DOI10.1080/10652469.2011.647015zbMath1257.35005OpenAlexW1985148882MaRDI QIDQ3144975

Hatem Mejjaoli

Publication date: 13 December 2012

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

Full work available at URL: https://doi.org/10.1080/10652469.2011.647015

zbMATH Keywords

distribution of the eigenvalueskernel reproducing theory

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Wave equation (35L05) Transform methods (e.g., integral transforms) applied to PDEs (35A22)

Related Items (11)

Time-frequency concentration and localization operators in the Dunkl setting ⋮ Phase space localized functions in the Dunkl setting ⋮ \((k,a)\)-generalized wavelet transform and applications ⋮ Reproducing kernel theory associated with the generalized Stockwell transform and applications ⋮ Uncertainty principles for the \(q\)-Bessel windowed transform and localization operators ⋮ \(L^p\) local uncertainty principles for the Dunkl Gabor transform on \(\mathbb{R}^d \) ⋮ \(k\)-Hankel Gabor transform and its applications to the theory of localization operators ⋮ Inversion theorem and quantitative uncertainty principles for the Dunkl Gabor transform on \({\mathbb{R}}^d\) ⋮ Dunkl-Stockwell transform and its applications to the time-frequency analysis ⋮ Dunkl-Gabor transform and time-frequency concentration ⋮ Sobolev spaces associated with a Dunkl type differential-difference operator on the real line and applications

Cites Work

• Unnamed Item
• Generalized Hermite polynomials and the heat equation for Dunkl operators
• The Dunkl transform
• Inversion of the Dunkl intertwining operator and its dual using Dunkl wavelets.
• Exact operator solution of the Calogero-Sutherland model
• Uncertainty principles for the continuous Dunkl Gabor transform and the Dunkl continuous wavelet transform
• Convolution operator and maximal function for the Dunkl transform
• Integral Kernels with Reflection Group Invariance
• The dunkel intertwining operator on spaces of functions and distributions and integral representation of its dual
• Dunkl Operator Formalism for Quantum Many-Body Problems Associated with Classical Root Systems
• Hypoellipticity and hypoanalyticity of the Dunkl Laplacian operator
• A positive radial product formula for the Dunkl kernel

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