Contributions to the hypergeometric function theory of Heckman and Opdam: Sharp estimates, Schwartz space, heat kernel
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Publication:2427043
DOI10.1007/s00039-008-0658-7zbMath1147.33004arXivmath/0605045OpenAlexW2086229321MaRDI QIDQ2427043
Publication date: 14 May 2008
Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0605045
Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Heat equation (35K05) Other functions coming from differential, difference and integral equations (33E30) Basic hypergeometric functions associated with root systems (33D67) Heat and other parabolic equation methods for PDEs on manifolds (58J35)
Related Items (65)
Opdam's hypergeometric functions: product formula and convolution structure in dimension 1 ⋮ The Dunkl-Laplace transform and Macdonald’s hypergeometric series ⋮ Harmonic Analysis Associated with the Heckman-Opdam-Jacobi Operator on $\mathbb{R}^{d+1}$ ⋮ Central limit theorems for random walks associated with hypergeometric functions of type BC ⋮ Elementary symmetric polynomials and martingales for Heckman-Opdam processes ⋮ An analogue to the Duistermaat-Kolk-Varadarajan estimate for the spherical functions associated with the root systems of type \(A\) ⋮ Uncertainty principles for the Heckman-Opdam transform ⋮ Paley-Wiener theorems of generalized Fourier transform associated with a Cherednik type operator on the real line ⋮ Spectral theorems associated with the Cherednik operators on \(\mathbb R^d\) ⋮ Intertwining operators associated to a family of differential-reflection operators ⋮ A new structure of an integral operator associated with trigonometric Dunkl settings ⋮ The Heckman-Opdam Markov processes ⋮ Dispersion and limit theorems for random walks associated with hypergeometric functions of type \(BC\) ⋮ Some martingales associated with multivariate Jacobi processes and Aomoto's Selberg integral ⋮ Integrability of conformal blocks. I: Calogero-Sutherland scattering theory ⋮ Hausdorff operators associated with the Opdam-Cherednik transform in Lebesgue spaces ⋮ Difference equation for the Heckman-Opdam hypergeometric function and its confluent Whittaker limit ⋮ Boundedness and compactness of Heckman-Opdam two-wavelet multipliers ⋮ Characterization for the spectrum of the hypergeometric Fourier transform in terms of the generalized resolvent function ⋮ Sharp estimates for the hypergeometric functions related to root systems of type $A$ and of rank $1$ ⋮ Integral kernels on complex symmetric spaces and for the Dyson Brownian Motion ⋮ Localization operators associated with the windowed Opdam–Cherednik transform on modulation spaces ⋮ Freezing limits for Calogero–Moser–Sutherland particle models ⋮ Qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces ⋮ Wavelet packet analysis in the framework of Heckman-Opdam theory on \(\mathbb{R}^d \) ⋮ Localization operators associated with the hypergeometric Wigner transform related to the Cherednik operators in the case of the root system \(BC_d\) ⋮ Uncertainty principles for the windowed Opdam–Cherednik transform ⋮ Theorems of Ingham and Chernoff on Riemannian symmetric spaces of noncompact type ⋮ The linear symmetric systems associated with the modified Cherednik operators and applications ⋮ Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications ⋮ Generalized symmetric systems and applications ⋮ Spectral theorems associated with the Jacobi-Cherednik operator ⋮ Localization operators and scalogram associated with the generalized continuous wavelet transform on $\mathbb{R}^d$ for the Heckman–Opdam theory ⋮ Ramanujan's master theorem for the hypergeometric Fourier transform associated with root systems ⋮ On the range of the generalized Fourier transform associated with a Cherednick type operator on the real line ⋮ An Introduction to Dunkl Theory and Its Analytic Aspects ⋮ The positivity of the hypergeometric translation operators associated to the Cherednik operators and the Heckman-Opdam theory on \(\mathbb{R}^d\) ⋮ Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC ⋮ Uncertainty principles for the Cherednik transform ⋮ Positivity of the Jacobi–Cherednik intertwining operator and its dual ⋮ Qualitative uncertainty principles for the Opdam–Cherednik transform ⋮ The Chébli–Trimèche hypergroups associated with the Dunkl and Heckman–Opdam theories ⋮ Cherednik-Sobolev spaces and applications ⋮ Generalized spaces of Sobolev types and applications ⋮ TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A CHEREDNIK TYPE OPERATOR ON THE REAL LINE ⋮ Integral representation and uniform limits for some Heckman-Opdam hypergeometric functions of type \textsl{BC} ⋮ The Wigner and Weyl transforms attached to the Heckman-Opdam-Jacobi theory on \(\mathbb{R}^{d+1}\) ⋮ Sharp estimates of radial Dunkl and heat kernels in the complex case \(A_n\) ⋮ Uncertainty principles for the Opdam–Cherednik transform on modulation spaces ⋮ Harmonic analysis associated with the Cherednik operators and the Heckman–Opdam theory ⋮ Generalized wavelet transform associated with the Heckman-Opdam-Jacobi theory on \(\mathbb{R}^{d+1}\) ⋮ The Cherednik and the Gaussian Cherednik Windowed transforms on $\mathbb{R}^d$ in the W-invariant case ⋮ GENERALIZED WAVELETS AND THE GENERALIZED WAVELET TRANSFORM ON ℝdFOR THE HECKMAN-OPDAM THEORY ⋮ QUALITATIVE UNCERTAINTY PRINCIPLES FOR THE INVERSE OF THE HYPERGEOMETRIC FOURIER TRANSFORM ⋮ THE POSITIVITY OF THE HYPERGEOMETRIC TRANSLATION OPERATORS ASSOCIATED TO THE CHEREDNIK OPERATORS AND THE HECKMAN-OPDAM THEORY ATTACHED TO THE ROOT SYSTEMS OF TYPE B2AND C2 ⋮ ABSOLUTE CONTINUITY OF THE REPRESENTING MEASURES OF THE HYPERGEOMETRIC TRANSLATION OPERATORS ATTACHED TO THE ROOT SYSTEM OF TYPE B2AND C2 ⋮ Time–frequency analysis associated with the generalized Wigner transform ⋮ Limit transition between hypergeometric functions of type BC and type A ⋮ Cowling-Price's and Hardy's uncertainty principles for the generalized Fourier transform associated to a Cherednik type operator on the real line ⋮ Qualitative uncertainty principles for the hypergeometric Fourier transform ⋮ The harmonic analysis associated to the Heckman-Opdam's theory and its application to a root system of type $BC_d$ ⋮ Weighted norm inequalities for the Opdam–Cherednik transform ⋮ Characterization of the support for the hypergeometric Fourier transform of the \(W\)-invariant functions and distributions on \(\mathbb R ^d\) and Roe's theorem ⋮ On the range of the Opdam-Cherednik transform and Roe's theorem in the Cherednik setting ⋮ Harmonic analysis associated with the modified Cherednik type operator and quantitative uncertainty principles for its Hartley transform
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