Experimental Mathematics

Stirling Numbers and Spin-Euler Polynomials

D. Eelbode

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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.

Article information

Experiment. Math., Volume 16, Issue 1 (2007), 55-66.

First available in Project Euclid: 5 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Fischer decomposition Hermitian Clifford analysis Stirling numbers


Eelbode, D. Stirling Numbers and Spin-Euler Polynomials. Experiment. Math. 16 (2007), no. 1, 55--66. https://projecteuclid.org/euclid.em/1175789801

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