Hardy's theorem and rotation for Dunkl transform

Sarathi Patra, Partha and Dogga, Venku Naidu (2021) Hardy's theorem and rotation for Dunkl transform. Complex Variables and Elliptic Equations, 66 (1). pp. 71-83. ISSN 1747-6933

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Abstract

We extend Hardy's theorem for rotation due to Lakey and Hogan for Dunkl transform associated with the reflection group (Formula presented.) in (Formula presented.) by using Dunkl-Hermite semigroup. In fact, we characterize (Formula presented.) by considering the decay of f and it's Dunkl transform (Formula presented.) along some lines in the complex plane, and we give a d-dimensional analogue for the same corresponding to the reflection group (Formula presented.) Moreover, we prove a version of Hardy's theorem, assuming the decay of Dunkl-Hermite coefficients.

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IITH Creators:
IITH CreatorsORCiD
Sarathi Patra, ParthaUNSPECIFIED
Dogga, Venku NaiduUNSPECIFIED
Item Type: Article
Uncontrolled Keywords: 20F55; 30D15; 39A70; 42A38; 43A25; Dunkl transform; Dunkl-Hermite semigroup; uncertainty principle
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: . LibTrainee 2021
Date Deposited: 30 Jul 2021 09:47
Last Modified: 30 Jul 2021 09:47
URI: http://raiith.iith.ac.in/id/eprint/8576
Publisher URL: http://doi.org/10.1080/17476933.2019.1704278
OA policy: https://v2.sherpa.ac.uk/id/publication/5091
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