Harmonic functions associated to Dunkl operators

DOI10.1007/s00605-007-0475-3zbMath1264.31002OpenAlexW2031474297MaRDI QIDQ2466849

El Hassan Youssfi, Mostafa Maslouhi

Publication date: 16 January 2008

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-007-0475-3

zbMATH Keywords

harmonic functionsPoisson kernelDunkl operatorsHarnack principle

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Boundary behavior of harmonic functions in higher dimensions (31B25) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20)

Related Items

Potential theory associated with the Dunkl Laplacian ⋮ Potential kernels for radial Dunkl Laplacians ⋮ Newtonian potentials and subharmonic functions associated to root systems ⋮ On the Green function and Poisson integrals of the Dunkl Laplacian ⋮ An Introduction to Dunkl Theory and Its Analytic Aspects ⋮ Mean value property of \(\Delta _k\)-harmonic functions on \(W\)-invariant open sets ⋮ Estimate of \(K\)-functionals and modulus of smoothness constructed by generalized spherical mean operator ⋮ Mean value properties for Dunkl-harmonic and Dunkl-polyharmonic functions ⋮ Wavelets invariant under finite reflection groups ⋮ An analog of Titchmarsh's Theorem for the Dunkl transform ⋮ A new mean value property for harmonic functions relative to the Dunkl-Laplacian operator and applications ⋮ Harmonic functions on metric measure spaces: Convergence and compactness ⋮ Green function and Poisson kernel associated to root systems for annular regions ⋮ On the generalized Poisson transform ⋮ Reflection groups in analysis and applications

Cites Work

• Generalized Hermite polynomials and the heat equation for Dunkl operators
• Reflection groups and orthogonal polynomials on the sphere
• Positivity of Dunkl's intertwining operator
• Integral Kernels with Reflection Group Invariance
• On a mean value property associated with the dunkl laplacian operator and applications
• The dunkel intertwining operator on spaces of functions and distributions and integral representation of its dual
• Poisson integrals associated to Dunkl operators for dihedral groups