207 citations · 2k across the 52 of their papers we have counts for
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Branching laws for spherical harmonics on superspaces in exceptional cases
Roman Lavicka
It turns out that harmonic analysis on the superspace R^{m|2n} is quite parallel to the classical theory on the Euclidean space R^{m} unless the superdimension M:=m-2n is even and…
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…
Separation of variables in the semistable range
Roman Lavicka
In this paper, we give an alternative proof of separation of variables for scalar-valued polynomials in the semistable range for the sy…
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 polynomials on superspace
Roman Lavicka, Dalibor Smid
Recently, the Fischer decomposition for polynomials on superspace R^{m|2n} (that is, polynomials in m commuting and 2n anti-commuting variables) has been obtained unless the superd…
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…