TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A CHEREDNIK TYPE OPERATOR ON THE REAL LINE

DOI10.1142/S0219530510001692zbMath1200.42003MaRDI QIDQ3056268

Mohamed Ali Mourou

Publication date: 11 November 2010

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

zbMATH Keywords

Paley-Wiener theoremtransmutation operatorsgeneralized convolutiondifferential-difference operators

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Integral transforms in distribution spaces (46F12) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Difference operators (39A70) Ordinary differential operators (34L99) General integral transforms (44A05)

Related Items (10)

Opdam's hypergeometric functions: product formula and convolution structure in dimension 1 ⋮ Paley-Wiener theorems of generalized Fourier transform associated with a Cherednik type operator on the real line ⋮ An elementary proof of the positivity of the intertwining operator in one-dimensional trigonometric Dunkl theory ⋮ Spectral theorems associated with the Jacobi-Cherednik operator ⋮ On the range of the generalized Fourier transform associated with a Cherednick type operator on the real line ⋮ Hardy and Cowling-Price theorems associated with the Jacobi-Cherednik operator ⋮ Qualitative uncertainty principles for the Opdam–Cherednik transform ⋮ Generalized spaces of Sobolev types and applications ⋮ Cowling-Price's and Hardy's uncertainty principles for the generalized Fourier transform associated to a Cherednik type operator on the real line ⋮ Harmonic analysis associated with the modified Cherednik type operator and quantitative uncertainty principles for its Hartley transform

Cites Work

• A new proof of a Paley-Wiener type theorem for the Jacobi transform
• 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
• TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A SINGULAR DIFFERENTIAL-DIFFERENCE OPERATOR ON THE REAL LINE
• Propriétés de la mesure spectrale pour une classe d'opérateurs différentiels singuliers sur [0,+∞[

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