A Quaternionic Analogue of the Segal–Bargmann Transform
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- 作者：K. Diki ; A. Ghanmi
- 关键词：Slice regular functions ; Slice hyperholomorphic Bargmann–Fock space ; Quaternionic Segal–Bargmann transform ; Left one ; dimensional quaternionic Fourier transform
- 刊名：Complex Analysis and Operator Theory
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：11
- 期：2
- 页码：457-473
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics, general; Operator Theory; Analysis;
- 出版者：Springer International Publishing
- ISSN：1661-8262
- 卷排序：11
文摘
The Bargmann–Fock space of slice hyperholomorphic functions is recently introduced by Alpay, Colombo, Sabadini and Salomon. In this paper, we reconsider this space and present a direct proof of its independence of the slice. We also introduce a quaternionic analogue of the classical Segal–Bargmann transform and discuss some of its basic properties. The explicit expression of its inverse is obtained and the connection to the left one-dimensional quaternionic Fourier transform is given.