Study of twisted Bargmann transform via Bargmann transform

Author:

Bais Shubham R.1,D Venku Naidu1

Affiliation:

1. Department of Mathematics , Indian Institute of Technology Hyderabad , Sangareddy , India

Abstract

Abstract In the present article, we give an alternate and easier proof for the image characterization of L 2 ( 2 n ) {L^{2}(\mathbb{R}^{2n})} under the twisted Bargmann transform which was earlier studied by Krontz, Thangavelu and Xu. As a consequence, we study some properties of the twisted Bergman spaces for 0 < p {0<p\leq\infty} and the L p {L^{p}} -boundedness of the twisted Bargmann transform, 1 p {1\leq p\leq\infty} . We also study L p {L^{p}} -boundedness of the twisted Bargmann projection P t {P_{t}} and the duality relations between the spaces B t p ( 2 n ) {B_{t}^{p}(\mathbb{C}^{2n})} , 1 < p < {1<p<\infty} .

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

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1. Application of Bargmann transform in the study of affine heat kernel transform;Journal of Pseudo-Differential Operators and Applications;2024-04-26

2. Integral representation of radial operators on the Bergman space over the unit disc;Journal of Mathematical Analysis and Applications;2024-03

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