A positive radial product formula for the Dunkl kernel
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Publication:4804218
DOI10.1090/S0002-9947-03-03235-5zbMath1015.33010arXivmath/0210137MaRDI QIDQ4804218
Publication date: 10 April 2003
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0210137
Convolution as an integral transform (44A35) Initial value problems for second-order hyperbolic equations (35L15) Orthogonal polynomials and functions associated with root systems (33C52)
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Cites Work
- Unnamed Item
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- Unnamed Item
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- Unnamed Item
- Unnamed Item
- Unnamed Item
- The product formula for the spherical functions on symmetric spaces in the complex case.
- Harmonic analysis of probability measures on hypergroups
- Spaces with an abstract convolution of measures
- Generalized Hermite polynomials and the heat equation for Dunkl operators
- Markov processes related with Dunkl operators
- The Dunkl transform
- An uncertainty principle for integral operators
- Positivity of Dunkl's intertwining operator
- Random walks with spherical symmetry
- Differential-Difference Operators Associated to Reflection Groups
- Integral Kernels with Reflection Group Invariance
- Integration of the intertwining operator for $h$-harmonic polynomials associated to reflection groups
- On a mean value property associated with the dunkl laplacian operator and applications
- The problem of lacunas and analysis on root systems
- Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators
- Intertwining Operators Associated to the Group S 3
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