POSITIVITY OF THE INTERTWINING OPERATOR AND HARMONIC ANALYSIS ASSOCIATED WITH THE JACOBI-DUNKL OPERATOR ON ${\mathbb R}$

DOI10.1142/S0219530503000247zbMath1056.43003OpenAlexW1974587392MaRDI QIDQ4474596

Maher Mili, F. Chouchane, Khalifa Trimèche

Publication date: 12 July 2004

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

Full work available at URL: https://doi.org/10.1142/s0219530503000247

zbMATH Keywords

Paley-Wiener theoremPlancherel theoremJacobi-Dunkl transformJacobi-Dunkl operatorJacobi-Dunkl convolution productPositivity of the Jacobi-Dunkl operator and its dual

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Difference operators (39A70) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

Related Items (33)

Qualitative uncertainty principles for the generalized Fourier transform associated to a Dunkl type operator on the real line ⋮ On the theorems of Hardy and Miyachi for the Jacobi–Dunkl transform ⋮ AnL^pversion of Hardy's theorem for the Jacobi–Dunkl transform ⋮ Some Results for the Jacobi-Dunkl Transform in the Space $L^{p}(mathbb{R},A_{alpha,beta}(x)dx)$ ⋮ Intertwining operators associated to a family of differential-reflection operators ⋮ A new aspect of generalized integral operator and an estimation in a generalized function theory ⋮ Convolution structure associated with the Jacobi-Dunkl operator on \(\mathbb R\) ⋮ Heisenberg inequalities for Jacobi transforms ⋮ Spectral properties of differential-difference symmetrized operators ⋮ Moduli of smoothness and generalized canonical Fourier-Bessel differential operator on the half-line ⋮ L^p–L^q-version of Morgan's theorem for the Jacobi–Dunkl transform ⋮ Qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces ⋮ Spectrum of functions and distributions for the Jacobi-Dunkl transform on \(\mathbb R\) ⋮ The linear symmetric systems associated with the modified Cherednik operators and applications ⋮ The finite continuous nonsymmetric Jacobi transform and applications ⋮ Generalized symmetric systems and applications ⋮ Hypercyclic and chaotic convolution associated with the Jacobi-Dunkl operator ⋮ New recurrence relations for Wilson polynomials via a system of Jacobi type orthogonal functions ⋮ Positivity of the Jacobi–Cherednik intertwining operator and its dual ⋮ The continuous wavelet transform associated with a differential-difference operator and applications ⋮ Harmonic analysis associated with the Jacobi-Dunkl operator on \(-\frac{\pi}{2},\frac{\pi}{2}[\)] ⋮ The Jacobi-Dunkl transform on \(\mathbb R\) and the convolution product on new spaces of distributions ⋮ The heat semigroup for the Jacobi-Dunkl operator and the related Markov processes ⋮ Uncertainty principles for the Opdam–Cherednik transform on modulation spaces ⋮ Equivalence of \(K\)-functionals and modulus of smoothness generated by a generalized Jacobi-Dunkl transform on the real line ⋮ Paley-Wiener theorem for a generalized Fourier transform associated to a Dunkl-type operator ⋮ Hilbert transform and related topics associated with Jacobi–Dunkl operators of compact and noncompact types ⋮ Uncertainty principles for the generalized Fourier transform associated to a Dunkl-type operator ⋮ A generalization of Miyachi's theorem ⋮ The heat and Poisson equations for the Jacobi-Dunkl generalized Laplacian ⋮ Sobolev spaces associated with a Dunkl type differential-difference operator on the real line and applications ⋮ Fractional Jacobi-Dunkl transform: properties and application ⋮ The transmutation operators relating to a Dunkl type operator on \(\mathbb{R}\) and their positivity

Cites Work

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• The spherical Fourier transform of rapidly decreasing functions. A simple proof of a characterization due to Harish-Chandra, Helgason, Trombi, and Varadarajan
• A new proof of a Paley-Wiener type theorem for the Jacobi transform
• Fourier transforms of Schwartz functions on Chébli-Trimèche hypergroups
• Paley-Wiener type theorems for a differential operator connected with symmetric spaces
• Opérateurs de transmutation et théorème de Paley–Wiener associés à un opérateur aux dérivées et différences sur
• Integral Kernels with Reflection Group Invariance
• Transmutation operators associated with a dunkl type differential-difference operator on the real line and certain of their applications
• TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A SINGULAR DIFFERENTIAL-DIFFERENCE OPERATOR ON THE REAL LINE
• A Note on the Quantum Rule of the Harmonic Oscillator

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