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] 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 …
Dunkl operators and a family of realizations of 𝔬𝔰𝔭 (1| 2)
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 …
$\mathfrak {osp}(1| 2) $ in the theory of Dunkl operators is obtained. This leads to a Dirac …
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 …
Pseudo‐differential operator in quaternion space
This paper introduces the quaternion Schwarz type space, and quaternion linear canonical
transform (QLCT) mapping properties are also discussed. Further, the quaternion pseudo …
transform (QLCT) mapping properties are also discussed. Further, the quaternion pseudo …
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 …
The Atiyah-Singer index theorem for a family of fractional Dirac operators on spin geometry
RA El-Nabulsi - Advances in Applied Clifford Algebras, 2023 - Springer
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 …
put across a kind of topological invariant (A^ genus) of a closed spin manifold M, hence …
The fractional Clifford-Fourier transform
H De Bie, N De Schepper - Complex analysis and operator theory, 2012 - Springer
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 …
on two numerical parameters. A series expansion for the kernel of the resulting integral …
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 …