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 …
Conformal symmetries of the super Dirac operator
K Coulembier, H De Bie - Revista matemática iberoamericana, 2015 - ems.press
Conformal symmetries of the super Dirac operator Page 1 Rev. Mat. Iberoam. 31 (2015), no. 2,
373–410 doi 10.4171/rmi/838 c European Mathematical Society Conformal symmetries of the …
373–410 doi 10.4171/rmi/838 c European Mathematical Society Conformal symmetries of the …
[PDF][PDF] Fundamental solutions for the super Laplace and Dirac operators and all their natural powers
H De Bie, F Sommen - arXiv preprint arXiv:0707.2862, 2007 - arxiv.org
arXiv:0707.2862v1 [math.AP] 19 Jul 2007 Fundamental solutions for the super Laplace and
Dirac operators and all their natural Page 1 arXiv:0707.2862v1 [math.AP] 19 Jul 2007 …
Dirac operators and all their natural Page 1 arXiv:0707.2862v1 [math.AP] 19 Jul 2007 …
(Discrete) Almansi type decompositions: an umbral calculus framework based on symmetries
N Faustino, G Ren - Mathematical methods in the applied …, 2011 - Wiley Online Library
We introduce the umbral calculus formalism for hypercomplex variables starting from the fact
that the algebra of multivariate polynomials shall be described in terms of the generators of …
that the algebra of multivariate polynomials shall be described in terms of the generators of …
q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials
K Coulembier, F Sommen - Journal of Physics A: Mathematical …, 2010 - iopscience.iop.org
We define a q-deformation of the Dirac operator, inspired by the one-dimensional q-
derivative. This implies a q-deformation of the partial derivatives. By taking the square of this …
derivative. This implies a q-deformation of the partial derivatives. By taking the square of this …
Introductory clifford analysis
H De Schepper, F Sommen - Operator theory, 2015 - biblio.ugent.be
In this chapter an introduction is given to Clifford analysis and the underlying Clifford
algebras. The functions under consideration are defined on Euclidean space and take …
algebras. The functions under consideration are defined on Euclidean space and take …
A Cauchy integral formula in superspace
H De Bie, F Sommen - Bulletin of the London Mathematical …, 2009 - academic.oup.com
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 …
established and amply investigated. In this paper a Cauchy integral formula is obtained in …
Schrödinger equation with delta potential in superspace
H De Bie - Physics Letters A, 2008 - Elsevier
A superspace version of the Schrödinger equation with a delta potential is studied using
Fourier analysis. An explicit expression for the energy of the single bound state is found as a …
Fourier analysis. An explicit expression for the energy of the single bound state is found as a …