40 citations · 307 across the 36 of their papers we have counts for
11 papers · 1 filter
The Cauchy Integral Formula in Hermitian, Quaternionic and osp(4|2) Clifford Analysis
Fred Brackx, Hennie De Schepper, Roman Lavicka +1
As is the case for the theory of holomorphic functions in the complex plane, the Cauchy Integral Formula has proven to be a corner stone of Clifford analysis, the monogenic functio…
Fischer decomposition for spinor valued polynomials in several variables
Roman Lavicka, Vladimir Soucek
It is well-known that polynomials decompose into spherical harmonics. This result is called separation of variables or the Fischer decomposition. In the paper we prove the Fischer…
Fischer Decomposition for osp(4|2)-monogenics in Quaternion Clifford Analysis
Fred Brackx, Hennie De Schepper, David Eelbode +2
Spaces of spinor-valued homogeneous polynomials, and in particular spaces of spinor-valued spherical harmonics, are decomposed in terms of irreducible representations of the symple…
The Radon transform between monogenic and generalized slice monogenic functions
Fabrizio Colombo, Roman Lavicka, Irene Sabadini +1
In [J. Bures, R. Lavicka, V. Soucek, Elements of quaternionic analysis and Radon transform, Textos de Matematica 42, Departamento de Matematica, Universidade de Coimbra, 2009], the…
Gelfand-Tsetlin Bases of Orthogonal Polynomials in Hermitean Clifford Analysis
F. Brackx, H. De Schepper, R. Lavicka +1
An explicit algorithmic construction is given for orthogonal bases for spaces of homogeneous polynomials, in the context of Hermitean Clifford analysis, which is a higher dimension…
The Cauchy-Kovalevskaya Extension Theorem in Hermitean Clifford Analysis
F. Brackx, H. De Schepper, R. Lavicka +1
Hermitean Clifford analysis is a higher dimensional function theory centered around the simultaneous null solutions, called Hermitean monogenic functions, of two Hermitean conjugat…