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Clifford Analysis and Harmonic Polynomials

In: Handbook of Geomathematics

Author

Listed:
  • Klaus Gürlebeck

    (Bauhaus-Universität Weimar)

  • Wolfgang Sprößig

    (TU Bergakademie Freiberg)

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.

Suggested Citation

  • Klaus Gürlebeck & Wolfgang Sprößig, 2015. "Clifford Analysis and Harmonic Polynomials," Springer Books, in: Willi Freeden & M. Zuhair Nashed & Thomas Sonar (ed.), Handbook of Geomathematics, edition 2, pages 2483-2525, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-54551-1_49
    DOI: 10.1007/978-3-642-54551-1_49
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