Clifford algebras, Fourier transforms, and quantum mechanics
H De Bie - Mathematical Methods in the Applied Sciences, 2012 - Wiley Online Library
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 …
related to either the Lie algebra or the Lie superalgebra. In the former case, one obtains …
[图书][B] Wavelet analysis: basic concepts and applications
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 …
introduction to the ideas underpinning wavelet theory and its diverse applications. This book …
[图书][B] Application of holomorphic functions in two and higher dimensions
K Gürlebeck, K Habetha, W Sprößig - 2016 - Springer
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 …
function theory have proven to be useful for the treatment of plane problems of mathematical …
[图书][B] Quaternion and Clifford Fourier Transforms
E Hitzer - 2021 - taylorfrancis.com
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 …
Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first …
History of quaternion and Clifford-Fourier transforms and wavelets
F Brackx, E Hitzer, SJ Sangwine - Quaternion and Clifford Fourier …, 2013 - Springer
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 …
several different threads, reflected in the overview of the subject presented in this chapter …
Clifford-valued linear canonical transform: convolution and uncertainty principles
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 …
has found many applications in optics, filter design, speech, image, video, and signal …
Quaternion and fractional Fourier transform in higher dimension
P Lian - Applied Mathematics and Computation, 2021 - Elsevier
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 …
years. In this paper, based on the symplectic decomposition of quaternions, we prove that …
Convolution products for hypercomplex Fourier transforms
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 …
of higher-dimensional signals such as color images. A main stumbling block for further …
On the Clifford short-time Fourier transform and its properties
A De Martino - Applied Mathematics and Computation, 2022 - Elsevier
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 …
Clifford setting. We prove some of the main properties of the Clifford short-time Fourier …
A new construction of the Clifford-Fourier kernel
D Constales, H De Bie, P Lian - Journal of Fourier Analysis and …, 2017 - Springer
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 …
Fourier transform. First, the kernel of the Clifford-Fourier transform in the Laplace domain is …