The Fourier and Hilbert transforms Under the Bargmann transform

被引：7

作者：

Dong, Xing-Tang ^{[1
]}

Zhu, Kehe ^{[2
,3
]}

机构：

[1] Tianjin Univ, Sch Math, Tianjin, Peoples R China

[2] Shantou Univ, Dept Math, Shantou, Peoples R China

[3] SUNY Albany, Dept Math & Stat, Albany, NY 12222 USA

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2018年 / 63卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Bargmann transform; Fock space; fractional Fourier transform; fractional Hilbert transform; wavelet transform; ANALYTIC-FUNCTIONS; SPACE;

D O I：

10.1080/17476933.2017.1324430

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

There is a canonical unitary transformation from L-2(R) onto the Fock space F-2, called the Bargmann transform. We study the action of the Bargmann transform on several classical integral operators on L-2(R), including the fractional Fourier transform, the fractional Hilbert transform and the wavelet transform.

引用

页码：517 / 531

页数：15

共 14 条

[1]

[Anonymous], 2001, Foundations of Time-Frequency Analysis, DOI DOI 10.1007/978-1-4612-0003-1

[2]

[Anonymous], 1989, ANN MATH STUDIES

[3] ON A HILBERT SPACE OF ANALYTIC FUNCTIONS AND AN ASSOCIATED INTEGRAL TRANSFORM .1. [J].