Abstract
Abstract In this paper boundary value problems for quaternionic Hermitian monogenic functions are presented using a circulant matrix approach. MSC:30G35.
Highlights
1 Introduction Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis
The theory is centred around the concept of monogenic functions, i.e. null solutions of a first-order vector-valued rotation invariant differential operator, called Dirac operator, which factorises the Laplacian; monogenic functions may be seen as a generalisation of holomorphic functions in the complex plane
Hermitian monogenic functions are considered, i.e. functions taking values either in a complex Clifford algebra or in complex spinor space, and being simultaneous null solutions of two complex Hermitian Dirac operators, which are invariant under the action of the unitary group
Summary
Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. Definition The ( × ) circulant matrix function G is called (left) Q-Hermitian monogenic in (or Q-monogenic for short) iff DT G = O in , where O denotes the matrix with zero entries. Left and right Qmonogenic matrix functions are called two-sided Q-monogenic.
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