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2007 Stirling Numbers and Spin-Euler Polynomials
D. Eelbode
Experiment. Math. 16(1): 55-66 (2007).

Abstract

The Fischer decomposition on $\mR^n$ gives the decomposition of arbitrary homogeneous polynomials in $n$ variables $(x_1,\dotsc,x_n)$ 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 $\mR^n$). 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 $\mR^{2n}$ involving complex Dirac operators commuting with the action of the unitary group.

Citation

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D. Eelbode. "Stirling Numbers and Spin-Euler Polynomials." Experiment. Math. 16 (1) 55 - 66, 2007.

Information

Published: 2007
First available in Project Euclid: 5 April 2007

zbMATH: 1201.30064
MathSciNet: MR2312977

Subjects:
Primary: 30G35‎
Secondary: 15A66 , 32W50

Keywords: Fischer decomposition , Hermitian Clifford analysis , Stirling numbers

Rights: Copyright © 2007 A K Peters, Ltd.

Vol.16 • No. 1 • 2007
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