Harmonic analysis associated with the Cherednik operators and the Heckman–Opdam theory

DOI10.1515/APAM.2011.022zbMath1207.33024OpenAlexW1972969476MaRDI QIDQ3074809

Khalifa Trimèche

Publication date: 10 February 2011

Published in: Advances in Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/apam.2011.022

zbMATH Keywords

Cherednik operatorshypergeometric Fourier transformhypergeometric translation operatorsHeckman-Opdam theoryhypergeometric convolution producttrigonometric Dunkl intertwining operator and its dual

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Other functions coming from differential, difference and integral equations (33E30) Other transforms and operators of Fourier type (43A32) Hypergeometric functions associated with root systems (33C67)

Related Items (19)

Harmonic Analysis Associated with the Heckman-Opdam-Jacobi Operator on $\mathbb{R}^{d+1}$ ⋮ Intertwining operators associated to a family of differential-reflection operators ⋮ The hypergroup associated with the Cherednik operators and applications to the infinitely divisible probabilities and convolution semigroups ⋮ Hausdorff operators associated with the Opdam-Cherednik transform in Lebesgue spaces ⋮ Boundedness and compactness of Heckman-Opdam two-wavelet multipliers ⋮ Wavelet packet analysis in the framework of Heckman-Opdam theory on \(\mathbb{R}^d \) ⋮ Localization operators and scalogram associated with the generalized continuous wavelet transform on $\mathbb{R}^d$ for the Heckman–Opdam theory ⋮ On the range of the generalized Fourier transform associated with a Cherednick type operator on the real line ⋮ The positivity of the hypergeometric translation operators associated to the Cherednik operators and the Heckman-Opdam theory on \(\mathbb{R}^d\) ⋮ Generalized wavelet transform associated with the Heckman-Opdam-Jacobi theory on \(\mathbb{R}^{d+1}\) ⋮ The Cherednik and the Gaussian Cherednik Windowed transforms on $\mathbb{R}^d$ in the W-invariant case ⋮ GENERALIZED WAVELETS AND THE GENERALIZED WAVELET TRANSFORM ON ℝ^dFOR THE HECKMAN-OPDAM THEORY ⋮ QUALITATIVE UNCERTAINTY PRINCIPLES FOR THE INVERSE OF THE HYPERGEOMETRIC FOURIER TRANSFORM ⋮ THE POSITIVITY OF THE HYPERGEOMETRIC TRANSLATION OPERATORS ASSOCIATED TO THE CHEREDNIK OPERATORS AND THE HECKMAN-OPDAM THEORY ATTACHED TO THE ROOT SYSTEMS OF TYPE B₂AND C₂ ⋮ ABSOLUTE CONTINUITY OF THE REPRESENTING MEASURES OF THE HYPERGEOMETRIC TRANSLATION OPERATORS ATTACHED TO THE ROOT SYSTEM OF TYPE B₂AND C₂ ⋮ Time–frequency analysis associated with the generalized Wigner transform ⋮ Qualitative uncertainty principles for the hypergeometric Fourier transform ⋮ The harmonic analysis associated to the Heckman-Opdam's theory and its application to a root system of type $BC_d$ ⋮ On the range of the Opdam-Cherednik transform and Roe's theorem in the Cherednik setting

Cites Work

• Unnamed Item
• Hypoelliptic dunkl convolution equations in the space of distributions on \({\mathbb R}^d\)
• Harmonic analysis for certain representations of graded Hecke algebras
• A unification of Knizhnik-Zamolodchikov and Dunkl operators via affine Hecke algebras
• Contributions to the hypergeometric function theory of Heckman and Opdam: Sharp estimates, Schwartz space, heat kernel

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