Zobrazeno 1 - 10
of 446
pro vyhledávání: '"Bie H"'
Publikováno v:
Lett. Math. Phys. 113 (2023), no. 5, article number 108
A model of the Bannai-Ito algebra in a superspace is introduced. It is obtained from the three-fold tensor product of the basic realization of the Lie superalgebra $osp(1|2)$ in terms of operators in one continuous and one Grassmanian variable. The b
Externí odkaz:
http://arxiv.org/abs/2306.02714
Publikováno v:
IMRN 2016, Issue 15, pp. 4649-4705
The Howe dual pair (sl(2),O(m)) allows the characterization of the classical Fourier transform (FT) on the space of rapidly decreasing functions as the exponential of a well-chosen element of sl(2) such that the Helmholtz relations are satisfied. In
Externí odkaz:
http://arxiv.org/abs/1411.6856
Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general principles, using 4 different yet equivalent definitions of the classica
Externí odkaz:
http://arxiv.org/abs/1101.1793
Autor:
De Bie, H., De Schepper, N.
We introduce the so-called Clifford-Gegenbauer polynomials in the framework of Dunkl operators, as well on the unit ball B(1), as on the Euclidean space $R^m$. In both cases we obtain several properties of these polynomials, such as a Rodrigues formu
Externí odkaz:
http://arxiv.org/abs/1003.1512
Autor:
De Bie, H., Xu, Y.
For functions that take values in the Clifford algebra, we study the Clifford-Fourier transform on $R^m$ defined with a kernel function $K(x,y) := e^{\frac{i \pi}{2} \Gamma_{y}}e^{-i }$, replacing the kernel $e^{i }$ of the ordinary Fourier
Externí odkaz:
http://arxiv.org/abs/1003.0689
In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1|2) in the theory of Dunkl operators is obtained. This leads to a Dirac operator depending on 3 parameters. Several function theoretical aspects of this op
Externí odkaz:
http://arxiv.org/abs/0911.4725
Publikováno v:
J. Phys. A: Math. Theor. 42 (2009) 395206.
In this paper, a new class of Cauchy integral formulae in superspace is obtained, using formal expansions of distributions. This allows to solve five open problems in the study of harmonic and Clifford analysis in superspace.
Externí odkaz:
http://arxiv.org/abs/0909.2544
The study of spherical harmonics in superspace, introduced in [J. Phys. A: Math. Theor. 40 (2007) 7193-7212], is further elaborated. A detailed description of spherical harmonics of degree k is given in terms of bosonic and fermionic pieces, which al
Externí odkaz:
http://arxiv.org/abs/0905.2092
Autor:
De Bie, H., Sommen, F.
In previous work the framework for a hypercomplex function theory in superspace was established and amply investigated. In this paper a Cauchy integral formula is obtained in this new framework by exploiting techniques from orthogonal Clifford analys
Externí odkaz:
http://arxiv.org/abs/0905.2085
Publikováno v:
In Journal of Approximation Theory October 2017 222:110-131
