Asymptotic analysis for the Dunkl kernel

DOI10.1006/jath.2002.3722zbMath1015.43004arXivmath/0202083OpenAlexW2171517382MaRDI QIDQ1867515

Margit Rösler, M. F. E. de Jeu

Publication date: 2 April 2003

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0202083

zbMATH Keywords

asymptoticsFourier transformsintertwining operatorconfluent hypergeometric functionDunkl kernelDunkl operators

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Measures on groups and semigroups, etc. (43A05) Applications of Lie (super)algebras to physics, etc. (17B81) Other transforms and operators of Fourier type (43A32)

Related Items

Newtonian potentials and subharmonic functions associated to root systems, Singular integrals in the rational Dunkl setting, Support properties of the intertwining and the mean value operators in Dunkl theory, Hardy spaces for the Dunkl harmonic oscillator, On the path integral formulation of Wigner–Dunkl quantum mechanics, An Introduction to Dunkl Theory and Its Analytic Aspects, Riesz potentials of Radon measures associated to reflection groups, Absolute continuity of the representing measures of the Dunkl intertwining operator and of its dual and applications, Schrödinger operators with reverse Hölder class potentials in the Dunkl setting and their Hardy spaces, On the estimates of Dunkl kernels, On semigroups generated by sums of even powers of Dunkl operators, The Hardy space \(H^1\) in the rational Dunkl setting, An estimate for the Dunkl kernels of type \(B_2 \), Dunkl transforms and Dunkl convolutions on functions and distributions with restricted growth, Paley–Wiener theorems for the Dunkl transform, Hörmander's multiplier theorem for the Dunkl transform, Reflection groups in analysis and applications, Revisiting Beurling's theorem for Fourier–Dunkl transform, Upper and lower bounds for Littlewood–Paley square functions in the Dunkl setting

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Le comportement à l'infini des fonctions de Bessel généralisées. I. (The behaviour at infinity of generalized Bessel functions.)
• Le comportement à l'infini des fonctions de Bessel généralisées. II. (The behaviour at infinity of generalized Bessel functions. II)
• Generalized Hermite polynomials and the heat equation for Dunkl operators
• The Dunkl transform
• Positivity of Dunkl's intertwining operator
• SHORT-TIME ESTIMATES FOR HEAT KERNELS ASSOCIATED WITH ROOT SYSTEMS
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• Singular Polynomials for Finite Reflection Groups
• Intertwining Operators Associated to the Group S 3
• Some theorems on perturbation theory. II
• On a Theorem of Bocher in the Theory of Ordinary Linear Differential Equations