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] Special functions of mathematical (geo-) physics
W Freeden, M Gutting - 2013 - Springer
Special functions enable us to formulate a scientific problem by reduction such that a new,
more concrete problem can be attacked within a well-structured framework, usually in the …
more concrete problem can be attacked within a well-structured framework, usually in the …
Random matrices with row constraints and eigenvalue distributions of graph Laplacians
P Akara-pipattana, O Evnin - Journal of Physics A: Mathematical …, 2023 - iopscience.iop.org
Symmetric matrices with zero row sums occur in many theoretical settings and in real-life
applications. When the offdiagonal elements of such matrices are iid random variables and …
applications. When the offdiagonal elements of such matrices are iid random variables and …
Type-B formal higher spin gravity
M Grigoriev, E Skvortsov - Journal of High Energy Physics, 2018 - Springer
A bstract We propose non-linear equations for the formal Type-B Higher Spin Gravity that is
dual to the free fermion or to the Gross-Neveu model, depending on the boundary …
dual to the free fermion or to the Gross-Neveu model, depending on the boundary …
[HTML][HTML] Divergence theorems and the supersphere
J Groeger - Journal of Geometry and Physics, 2014 - Elsevier
The transformation formula of the Berezin integral holds, in the non-compact case, only up to
boundary integrals, which have recently been quantified by Alldridge–Hilgert–Palzer. We …
boundary integrals, which have recently been quantified by Alldridge–Hilgert–Palzer. We …
Spherical harmonics and integration in superspace: II
The study of spherical harmonics in superspace, introduced in (De Bie and Sommen 2007 J.
Phys. A: Math. Theor. 40 7193) is further elaborated. A detailed description of spherical …
Phys. A: Math. Theor. 40 7193) is further elaborated. A detailed description of spherical …
Fourier transform and related integral transforms in superspace
H De Bie - Journal of Mathematical Analysis and Applications, 2008 - Elsevier
In this paper extensions of the classical Fourier, fractional Fourier and Radon transforms to
superspace are studied. Previously, a Fourier transform in superspace was already studied …
superspace are studied. Previously, a Fourier transform in superspace was already studied …
Integration in superspace using distribution theory
K Coulembier, H De Bie… - Journal of Physics A …, 2009 - iopscience.iop.org
Integration in superspace using distribution theory Page 1 Journal of Physics A:
Mathematical and Theoretical Integration in superspace using distribution theory To cite this …
Mathematical and Theoretical Integration in superspace using distribution theory To cite this …
Applied and Numerical Harmonic Analysis
JJ Benedetto - (No Title), 2007 - Springer
Frame theory is nowadays a fundamental research area in mathematics, computer science,
and engineering with many exciting applications in a variety of different fields. Introduced in …
and engineering with many exciting applications in a variety of different fields. Introduced in …
[HTML][HTML] The metaplectic Howe duality and polynomial solutions for the symplectic Dirac operator
H De Bie, P Somberg, V Souček - Journal of Geometry and Physics, 2014 - Elsevier
We study various aspects of the metaplectic Howe duality realized by the Fischer
decomposition for the metaplectic representation space of polynomials on R 2 n valued in …
decomposition for the metaplectic representation space of polynomials on R 2 n valued in …