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Stirling numbers and spin-Euler polynomials. (English) Zbl 1201.30064
Summary: The Fischer decomposition on \(\mathbb R^n\) gives the decomposition of arbitrary homogeneous polynomials in \(n\) variables \(x_1,\ldots,x_n\) in terms of harmonic homogeneous polynomials. In classical Clifford analysis a refinement was obtained, giving a decomposition in terms of monogenic polynomials, i.e., homogeneous null solutions for the Dirac operator (a vector-valued differential operator factorizing the Laplacian \(\Delta_n\) on \(\mathbb R^n\)). In this paper the building blocks for the Fischer decomposition in the Hermitian Clifford setting are determined, yielding a new refinement of harmonic analysis on \(\mathbb R^{2n}\) involving complex Dirac operators commuting with the action of the unitary group.

MSC:
30G35 Functions of hypercomplex variables and generalized variables
32W50 Other partial differential equations of complex analysis in several variables
15A66 Clifford algebras, spinors
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