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 …

Wavelet Analysis: Basic Concepts and Applications provides a basic and self-contained
introduction to the ideas underpinning wavelet theory and its diverse applications. This book …

Complex analysis is one of the most interesting areas in mathematics. Methods of complex
function theory have proven to be useful for the treatment of plane problems of mathematical …

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 …

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 …

Linear canonical transform is a three-parameter class of linear integral transformation, which
has found many applications in optics, filter design, speech, image, video, and signal …

Several quaternion Fourier transforms have received considerable attention in the last
years. In this paper, based on the symplectic decomposition of quaternions, we prove that …

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 …

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 …