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On an orthonormal basis of solid spherical monogenics recursively generated by anti-holomorphic \(\bar z\)-powers. (English) Zbl 1191.30017

Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics, Rethymno, Crete, Greece, September 18–22, 2009. Vol. 2. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0708-4/hbk; 978-0-7354-0709-1/set). AIP Conference Proceedings 1168, 2, 765-768 (2009).
In his dissertation paper, S. Bock found an orthogonal system of inner solid spherical monogenics in \(L^2(B_3^+;\mathbb H\cap\ker\partial)\). In a preceding paper, the authors could prove new efficient recurrence formulae for inner and corresponding outer spherical monogenics. In particular, a simple representation for the monogenic constants follows. The action of the hypercomplex derivative on the system is studied. Nice and very natural explicit formulae are obtained.
For the entire collection see [Zbl 1177.00116].

MSC:

30G35 Functions of hypercomplex variables and generalized variables
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