In this review, we give an overview of several recent generalizations of the Fourier transform,
related to either the Lie algebra or the Lie superalgebra. In the former case, one obtains …

Quaternion and Clifford Fourier Transforms describes the development of quaternion and
Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first …

In this paper, a family of radial deformations of the realization of the Lie superalgebra
$\mathfrak {osp}(1| 2) $ in the theory of Dunkl operators is obtained. This leads to a Dirac …

The development of hypercomplex Fourier transforms and wavelets has taken place in
several different threads, reflected in the overview of the subject presented in this chapter …

This paper introduces the quaternion Schwarz type space, and quaternion linear canonical
transform (QLCT) mapping properties are also discussed. Further, the quaternion pseudo …

Hypercomplex Fourier transforms are increasingly used in signal processing for the analysis
of higher-dimensional signals such as color images. A main stumbling block for further …

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 …

Abstract The Atiyah-Singer index formula for Dirac operators acting on the space of spinors
put across a kind of topological invariant (A^ genus) of a closed spin manifold M, hence …

In this paper, a fractional version of the Clifford-Fourier transform is introduced, depending
on two numerical parameters. A series expansion for the kernel of the resulting integral …

In this paper, we develop a new method based on the Laplace transform to study the Clifford-
Fourier transform. First, the kernel of the Clifford-Fourier transform in the Laplace domain is …