An Introduction to Dunkl Theory and Its Analytic Aspects
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Publication:4644991
DOI10.1007/978-3-319-52842-7_1zbMath1404.33014arXiv1611.08213OpenAlexW2558618416MaRDI QIDQ4644991
Publication date: 9 January 2019
Published in: Trends in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1611.08213
Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Basic hypergeometric functions associated with root systems (33D67) Hypergeometric functions associated with root systems (33C67)
Related Items
Harmonic Analysis Associated with the Heckman-Opdam-Jacobi Operator on $\mathbb{R}^{d+1}$ ⋮ Free boson realization of the Dunkl intertwining operator in one dimension ⋮ Positive \(L^p\)-bounded Dunkl-type generalized translation operator and its applications ⋮ Rellich, Gagliardo-Nirenberg, Trudinger and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applications ⋮ Matrix addition and the Dunkl transform at high temperature ⋮ \(L^p\) Hardy's identities and inequalities for Dunkl operators ⋮ Hardy-Sobolev inequalities with Dunkl weights ⋮ Sharp estimates for the hypergeometric functions related to root systems of type $A$ and of rank $1$ ⋮ Dimension‐free square function estimates for Dunkl operators ⋮ Sharp estimates for \(W\)-invariant Dunkl and heat kernels in the \(A_n\) case ⋮ Freezing limits for Calogero–Moser–Sutherland particle models ⋮ Asymptotic estimates for the growth of deformed Hankel transform by modulus of continuity ⋮ Weighted Bergman kernels for nearly holomorphic functions on bounded symmetric domains ⋮ Sharp Li-Yau inequalities for Dunkl harmonic oscillators ⋮ Inversion formula for the hypergeometric Fourier transform associated with a root system of type \(BC\) ⋮ A Laplace-type representation for some generalized spherical functions of type $BC$ ⋮ Exotic multiplicity functions and heat maximal operators in certain Dunkl settings ⋮ Central limit theorems for multivariate Bessel processes in the freezing regime ⋮ The Dunkl kernel and intertwining operator for dihedral groups ⋮ Limit theorems for multivariate Bessel processes in the freezing regime ⋮ Dunkl intertwining operator for symmetric groups ⋮ Generalized wavelet transform associated with the Heckman-Opdam-Jacobi theory on \(\mathbb{R}^{d+1}\) ⋮ Behavior of eigenvalues of certain Schrödinger operators in the rational Dunkl setting ⋮ Relative Nash-type and \(L^2\)-Sobolev inequalities in Dunkl setting ⋮ Limit theorems for Bessel and Dunkl processes of large dimensions and free convolutions ⋮ Infinite dimensional systems of particles with interactions given by Dunkl operators ⋮ The Harish-Chandra integral: an introduction with examples ⋮ Logarithmic Sobolev inequalities for Dunkl operators with applications to functional inequalities for singular Boltzmann-Gibbs measures ⋮ Freezing limits for beta-Cauchy ensembles ⋮ Sobolev-type inequalities for Dunkl operators ⋮ Hardy-type inequalities for Dunkl operators with applications to many-particle Hardy inequalities
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Cites Work
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