Clifford Analysis and Harmonic Polynomials

Klaus Gürlebeck () and Wolfgang Sprößig ()
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Klaus Gürlebeck: Bauhaus-Universität Weimar
Wolfgang Sprößig: TU Bergakademie Freiberg

A chapter in Handbook of Geomathematics, 2015, pp 2483-2525 from Springer

Abstract: Abstract This overview gives an insight in the new field of hypercomplex analysis in relation to harmonic analysis. The algebra of complex numbers is replaced by the non-commutative algebra of real quaternions or by Clifford algebras. This contribution is focused on the presentation of an operator calculus on the sphere as well as the discussion of monogenic and holomorphic orthonormal systems of polynomials and special functions on the unit ball and the sphere. Function theoretic elements are lined out. Relations to the Lie algebra SO(3) are discussed and a corresponding Radon transform is introduced.

Keywords: Radon Transform; Clifford Algebra; Real Quaternions; Riesz System; Gegenbauer Functions (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-54551-1_49

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DOI: 10.1007/978-3-642-54551-1_49

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