Generalized multidimensional Hilbert transforms in Clifford analysis.
Hermitean Téodorescu transform decomposition of continuous matrix functions on fractal hypersurfaces.
Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces.
Finite element approximation of a contact vector eigenvalue problem
We consider a nonstandard elliptic eigenvalue problem of second order on a two-component domain consisting of two intervals with a contact point. The interaction between the two domains is expressed through a coupling condition of nonlocal type, more specifically, in integral form. The problem under consideration is first stated in its variational form and next interpreted as a second-order differential eigenvalue problem. The aim is to set up a finite element method for this problem. The error...
Fischer decompositions in Euclidean and Hermitean Clifford analysis
Euclidean Clifford analysis is a higher dimensional function theory studying so–called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator . In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure on Euclidean space and a corresponding second Dirac operator , leading to the system of equations expressing so-called Hermitean monogenicity. The invariance of this...
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