Linear Canonical Bargmann Transform

Rong Qian Linghu; Bing Zhao Li

doi:10.1007/s11785-024-01628-9

Linear Canonical Bargmann Transform

Rong Qian Linghu
, Bing Zhao Li^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, a linear canonical transform associated with the Bargmann transform, referred to as the linear canonical Bargmann transform (LCBT) is proposed. The relationship between the Fourier transform, fractional Fourier transform, and the LCBT are discussed. Following this, the basic properties of the LCBT are derived, including the Parseval theorem, linearity, translation, modulation, convolution, and the uncertainty principle. It is evident that the LCBT serves as a generalized form of both the Fourier transform and fractional Fourier transform.

Original language	English
Article number	7
Journal	Complex Analysis and Operator Theory
Volume	19
Issue number	1
DOIs	https://doi.org/10.1007/s11785-024-01628-9
Publication status	Published - Dec 2024

Keywords

Bargmann transform
Convolution
Linear canonical Bargmann transform
Uncertainty principle

Access to Document

10.1007/s11785-024-01628-9

Cite this

@article{4d09af53305548928ed67c77c42691f6,

title = "Linear Canonical Bargmann Transform",

abstract = "In this paper, a linear canonical transform associated with the Bargmann transform, referred to as the linear canonical Bargmann transform (LCBT) is proposed. The relationship between the Fourier transform, fractional Fourier transform, and the LCBT are discussed. Following this, the basic properties of the LCBT are derived, including the Parseval theorem, linearity, translation, modulation, convolution, and the uncertainty principle. It is evident that the LCBT serves as a generalized form of both the Fourier transform and fractional Fourier transform.",

keywords = "Bargmann transform, Convolution, Linear canonical Bargmann transform, Uncertainty principle",

author = "Linghu, \{Rong Qian\} and Li, \{Bing Zhao\}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.",

year = "2024",

month = dec,

doi = "10.1007/s11785-024-01628-9",

language = "English",

volume = "19",

journal = "Complex Analysis and Operator Theory",

issn = "1661-8254",

publisher = "Springer International Publishing",

number = "1",

}

TY - JOUR

T1 - Linear Canonical Bargmann Transform

AU - Linghu, Rong Qian

AU - Li, Bing Zhao

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

PY - 2024/12

Y1 - 2024/12

N2 - In this paper, a linear canonical transform associated with the Bargmann transform, referred to as the linear canonical Bargmann transform (LCBT) is proposed. The relationship between the Fourier transform, fractional Fourier transform, and the LCBT are discussed. Following this, the basic properties of the LCBT are derived, including the Parseval theorem, linearity, translation, modulation, convolution, and the uncertainty principle. It is evident that the LCBT serves as a generalized form of both the Fourier transform and fractional Fourier transform.

AB - In this paper, a linear canonical transform associated with the Bargmann transform, referred to as the linear canonical Bargmann transform (LCBT) is proposed. The relationship between the Fourier transform, fractional Fourier transform, and the LCBT are discussed. Following this, the basic properties of the LCBT are derived, including the Parseval theorem, linearity, translation, modulation, convolution, and the uncertainty principle. It is evident that the LCBT serves as a generalized form of both the Fourier transform and fractional Fourier transform.

KW - Bargmann transform

KW - Convolution

KW - Linear canonical Bargmann transform

KW - Uncertainty principle

UR - https://www.scopus.com/pages/publications/85211129329

U2 - 10.1007/s11785-024-01628-9

DO - 10.1007/s11785-024-01628-9

M3 - Article

AN - SCOPUS:85211129329

SN - 1661-8254

VL - 19

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

IS - 1

M1 - 7

ER -

Linear Canonical Bargmann Transform

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this