A Quaternionic Analogue of the Segal-Bargmann Transform

被引：24
|
作者：
Diki, K. [1 ]
Ghanmi, A. [1 ]
机构：
[1] Mohammed V Univ Rabat, PDE & Spectral Geometry, Lab Anal & Applicat, URAC 03,Dept Math,Fac Sci, POB 1014, Rabat, Morocco
来源：
COMPLEX ANALYSIS AND OPERATOR THEORY | 2017年 / 11卷 / 02期
关键词：
Slice regular functions; Slice hyperholomorphic Bargmann-Fock space; Quaternionic Segal-Bargmann transform; Left one-dimensional quaternionic Fourier transform; REGULAR FUNCTIONS; SPACE;
D O I：
10.1007/s11785-016-0609-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：457 / 473
页数：17
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