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 - http://www.scopus.com/inward/record.url?scp=85211129329&partnerID=8YFLogxK
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 -