On the images of Dunkl–Sobolev spaces under the Schrödinger semigroup associated to Dunkl operators

C, Sivarama krishnan and D, Sukumar and D, Venku Naidu (2017) On the images of Dunkl–Sobolev spaces under the Schrödinger semigroup associated to Dunkl operators. Journal of Pseudo-Differential Operators and Applications. pp. 1-18. ISSN 1662-9981

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Abstract

In this article, we consider the Schrödinger semigroup related to the Dunkl–Laplacian Δμ (associated to finite reflection group G) on Rn. We characterize the image of L2(Rn,eu2hμ(u)du) under the Schrödinger semigroup as a reproducing kernel Hilbert space. We define Dunkl–Sobolev space in L2(Rn,eu2hμ(u)du) and characterize it’s image under the Schrödinger semigroup associated to G=Zn2 as a reproducing kernel Hilbert space up to equivalence of norms. Also we provide similar results for Schrödinger semigroup associated to Dunkl–Hermite operator.

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IITH Creators:	IITH Creators ORCiD D, Sukumar UNSPECIFIED
Item Type:	Article
Uncontrolled Keywords:	Segal–Bargmann, transform Schrödinger semigroup, Weighted Bergman space, Dunkl–Sobolev space
Subjects:	Mathematics
Divisions:	Department of Mathematics
Depositing User:	Team Library
Date Deposited:	30 Jul 2018 10:08
Last Modified:	30 Jul 2018 10:08
URI:	http://raiithold.iith.ac.in/id/eprint/4333
Publisher URL:	http://doi.org/10.1007/s11868-017-0233-9
OA policy:	http://www.sherpa.ac.uk/romeo/issn/1662-9981/
Related URLs:	Google Scholar

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