Support properties of the intertwining and the mean value operators in Dunkl theory

DOI10.1090/proc/13478zbMath1380.31005OpenAlexW2744331433MaRDI QIDQ4590972

Chaabane Rejeb, Léonard Gallardo

Publication date: 21 November 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13478

zbMATH Keywords

Dunkl operatorDunkl harmonic functionsrepresenting measuresDunkl's intertwining operator

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Harmonic, subharmonic, superharmonic functions on other spaces (31C05)

Related Items (9)

Dunkl translations, Dunkl-type BMO space, and Riesz transforms for the Dunkl transform on \(L^\infty \) ⋮ Unnamed Item ⋮ Imaginary powers of \((k, 1)\)-generalized harmonic oscillator ⋮ Newtonian potentials and subharmonic functions associated to root systems ⋮ Remarks on Dunkl translations of non-radial kernels ⋮ A Laplace-type representation for some generalized spherical functions of type $BC$ ⋮ An Introduction to Dunkl Theory and Its Analytic Aspects ⋮ Riesz potentials of Radon measures associated to reflection groups ⋮ Upper and lower bounds for the Dunkl heat kernel

Cites Work

• The Dunkl transform
• Asymptotic analysis for the Dunkl kernel
• Positivity of Dunkl's intertwining operator
• A uniform proof of the Macdonald-Mehta-Opdam identity for finite Coxeter groups
• SHORT-TIME ESTIMATES FOR HEAT KERNELS ASSOCIATED WITH ROOT SYSTEMS
• A new mean value property for harmonic functions relative to the Dunkl-Laplacian operator and applications
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres
• The dunkel intertwining operator on spaces of functions and distributions and integral representation of its dual
• Reflection groups and invariant theory
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