760 research outputs found
A Paley-Wiener theorem for the inverse Fourier transform on some homogeneous spaces
We formulate and prove a version of Paley-Wiener theorem for the inverse
Fourier transform on non-compact Riemannian symmetric spaces and Heisenberg
groups. The main ingredient in the proof is the Gutzmer's formula.Comment: 17 page
An analogue of Gutzmer's formula for Hermite expansions
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 semigroup. We also obtain some new orthogonality
relations for complexified Hermite functions.Comment: 15 page
Heat kernel transform for nilmanifolds associated to the Heisenberg group
We study the heat kernel transform on a nilmanifold of the Heisenberg
group. We show that the image of under this transform is a direct
sum of weighted Bergman spaces which are related to twisted Bergman and
Hermite-Bergman spaces.Comment: Revised version; to appear in Revista Mathematica Iberoamericana, 28
Mixed norm estimates for the Riesz transforms associated to Dunkl harmonic oscillators
In this paper we study weighted mixed norm estimates for Riesz transforms
associated to Dunkl harmonic oscillators. The idea is to show that the required
inequalities are equivalent to certain vector valued inequalities for operator
defined in terms of Laguerre expansions. In certain cases the main result can
be deduced from the corresponding result for Hermite Riesz transforms.Comment: 25 page
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