Linear Canonical Bargmann Transform

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.