关于一类指数函数的复傅里叶变换的零点

一类指数函数复傅里叶变换的几何解释

On the Geometric Interpretation of the Complex Fourier Transforms of a Class of Exponential Functions

从几何角度研究了一类零点全部在实直线上的指数函数的复傅里叶变换。这些变换都属于Laguerre - Polya变换类，并证明了它们的零点都是单的.

Fourier transform for functions of bicomplex variables

This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this bicomplex version of Fourier transform are examined.

Bicomplex analogs of Segal-Bargmann and fractional Fourier transforms

We consider and discuss some basic properties of the bicomplex analog of the classical Bargmann space. The explicit expression of the integral operator connecting the complex and bicomplex Bargmann spaces is also given. The corresponding bicomplex Segal--Bargmann transform is introduced and studied as well. Its explicit expression as well as the one of its inverse are then used to introduce a class of two--parameter bicomplex Fourier transforms (bicomplex fractional Fourier transform). This approach is convenient in exploring some useful properties of this bicomplex fractional Fourier transfor…

The Fourier and Hilbert transforms under the Bargmann transform

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.

从离散到连续非线性傅里叶变换的收敛性

Convergence from the discrete to the continuous non-linear Fourier transform

该研究借助复函数论与谱问题的关联新视角，探究离散到连续非线性傅里叶变换的收敛性，指出微分算子谱问题视角下的相关结果与离散情形的收敛问题具有相似性。

On the Clifford short-time Fourier transform and its properties

In this paper we investigate how the short-time Fourier transform can be extended in a Clifford setting. We prove some of the main properties of the Clifford short-time Fourier transform such as the orthogonality relation, the reconstruction property and the reproducing kernel formula. Moreover, we show the effects of modulating and translating the signal and the window function, respectively. Finally, we demonstrate the Lieb's uncertainty principle for the Clifford short-time Fourier transform.