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An analogue of Gutzmer's formula for Hermite expansions
S. Thangavelu
We prove an analogue of Gutzmer's formula for Hermite expansions. As a consequence we obtain a new proof of a characterisation of the image of under the Hermite semig…
Riesz transform and Riesz potentials for Dunkl transform
Sundaram Thangavelu, Yuan Xu
Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflect…
Convolution operator and maximal function for Dunkl transform
Sundaram Thangavelu, Yuan Xu
For a family of weight functions, , invariant under a finite reflection group on $\RR^d$, analysis related to the Dunkl transform is carried out for the weighted spaces.…
The heat kernel transform for the Heisenberg group
Bernhard Kroetz, Sundaram Thangavelu, Yuan Xu
The heat kernel transform H_t for the Heisenberg group is studied in detail. The main result shows that the image of H_t is a direct sum of two weighted Bergman spaces whose associ…