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Zbl 1121.15027
Anghel, Nicolae
Projecting on polynomial Dirac spinors.
(English)
[A] Mladenov, Iva\"ilo (ed.) et al., Proceedings of the 8th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 9--14, 2006. Sofia: Bulgarian Academy of Sciences. 121-126 (2007). ISBN 978-954-8495-37-0/pbk

Summary: We adapt {\it S. Axler} and {\it W. Ramey}'s method [Proc. Am. Math. Soc. 123, No. 12, 3765--3773 (1995; Zbl 0848.31002)] of constructing the harmonic part of a homogeneous polynomial to the Fischer decomposition associated to Dirac operators acting on polynomial spinors. The result yields a constructive solution to a Dirichlet-like problem with polynomial boundary data.
MSC 2000:
*15A66 Clifford algebras
31B05 Harmonic functions, etc. (higher-dimensional)
31B20 Boundary value and inverse problems (higher-dim. potential theory)
81R25 Spinor and twistor methods in quantum theory

Keywords: homogeneous polynomial; Fischer decomposition; Dirac operators; polynomial spinors; Dirichlet-like problem; polynomial boundary data

Citations: Zbl 0848.31002

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