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.

引用

页码：457 / 473

页数：17

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