Intertwining operators associated to a family of differential-reflection operators

DOI10.1007/s00009-016-0736-2zbMath1364.34093OpenAlexW4298858559MaRDI QIDQ346885

Asma Boussen, Salem Ben Said, Mohamed Sifi

Publication date: 30 November 2016

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-016-0736-2

zbMATH Keywords

intertwining operatorsspectral problemdifferential-reflection operators

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) General theory of ordinary differential operators (47E05) Other functions coming from differential, difference and integral equations (33E30) Spectral theory of functional-differential operators (34K08)

Related Items (2)

\(L^p\) harmonic analysis for differential-reflection operators ⋮ \(L^{p}\)-Fourier analysis for certain differential-reflection operators

Cites Work

• Singularities and analytic continuation of the Dunkl and the Jacobi-Cherednik intertwining operators and their duals
• \(L^{p}\)-Fourier analysis for certain differential-reflection operators
• Transformation intégrale de Weyl et théorème de Paley-Wiener associes à un opérateur différentiel singulier sur \((0,\infty)\)
• Convolution structure associated with the Jacobi-Dunkl operator on \(\mathbb R\)
• Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators
• Markov processes related with Dunkl operators
• The Dunkl transform
• \(L^p\) harmonic analysis for differential-reflection operators
• Sur un théorème de Paley-Wiener associe à la décomposition spectrale d'un opérateur de Sturm-Liouville sur \([0, \infty\)]
• Harmonic analysis for certain representations of graded Hecke algebras
• Positivity of Dunkl's intertwining operator
• A unification of Knizhnik-Zamolodchikov and Dunkl operators via affine Hecke algebras
• The transmutation operators relating to a Dunkl type operator on \(\mathbb{R}\) and their positivity
• Contributions to the hypergeometric function theory of Heckman and Opdam: Sharp estimates, Schwartz space, heat kernel
• An elementary approach to the hypergeometric shift operators of Opdam
• Opdam's hypergeometric functions: product formula and convolution structure in dimension 1
• Harmonic analysis associated with the Cherednik operators and the Heckman–Opdam theory
• Opérateurs de Delsarte et problèmes mixtes
• Positivity of the Jacobi–Cherednik intertwining operator and its dual
• Absolute continuity of the representing measures of the Dunkl intertwining operator and of its dual and applications
• Differential-Difference Operators Associated to Reflection Groups
• TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A SINGULAR DIFFERENTIAL-DIFFERENCE OPERATOR ON THE REAL LINE
• POSITIVITY OF THE INTERTWINING OPERATOR AND HARMONIC ANALYSIS ASSOCIATED WITH THE JACOBI-DUNKL OPERATOR ON ${\mathbb R}$
• Positivity of the transmutation operators associated with a Cherednik type operator on the real line
• Orthogonal Polynomials of Several Variables
• Théoreme de Paley-Wiener associe à un opérateur différentiel singulier sur \((0,+\infty)\)
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