Hypoellipticity and hypoanalyticity of the Dunkl Laplacian operator

DOI10.1080/10652460412331270689zbMath1071.33014OpenAlexW2082143501MaRDI QIDQ4659494

Khalifa Trimèche, Hatem Mejjaoli

Publication date: 21 March 2005

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460412331270689

zbMATH Keywords

hypoellipticityDunkl Laplacian operatorhypoanalyticity

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Hypoelliptic equations (35H10)

Related Items

Nonlinear Dunkl-wave equations, On the Dirichlet problem associated with the Dunkl Laplacian, Potential theory associated with the Dunkl Laplacian, Nonlinear generalized Dunkl-wave equations and applications, Reproducing kernel theory associated with the generalized Stockwell transform and applications, Direct and inverse problems for time-fractional heat equation generated by Dunkl operator, Solution of Integral Equations by Dunkl and Distributional Dunkl Transform, A variant of Cowling-Price's theorem for the Dunkl transform on \(\mathbb R\), Mean value property of \(\Delta _k\)-harmonic functions on \(W\)-invariant open sets, Cherednik-Sobolev spaces and applications, Generalized spaces of Sobolev types and applications, New Type Paley-Wiener Theorems for the Dunkl Transform on R, Dunkl-Stockwell transform and its applications to the time-frequency analysis, Dunkl heat semigroup and applications, Clifford analysis for finite reflection groups, Unnamed Item, Sobolev spaces associated with a Dunkl type differential-difference operator on the real line and applications, Practical inversion formulas for the Dunkl–Gabor transform on ℝ^d

Cites Work

• The Dunkl transform
• Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement
• Exact operator solution of the Calogero-Sutherland model
• An elementary approach to the hypergeometric shift operators of Opdam
• Integral Kernels with Reflection Group Invariance
• Common algebraic structure for the Calogero - Sutherland models
• 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
• Dunkl Operator Formalism for Quantum Many-Body Problems Associated with Classical Root Systems
• Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators