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Bounded monogenic functions on unbounded domains. (English) Zbl 0890.30034
Ramírez de Arellano, E. (ed.) et al., Operator theory for complex and hypercomplex analysis. Proceedings of a conference, Mexico City, Mexico, December 12–17, 1994. Providence, RI: American Mathematical Society. Contemp. Math. 212, 71-79 (1998).
Summary: A minor modification of the Clifford Cauchy kernel is introduced. This kernel works extremely well at transposing results from Clifford analysis over bounded domains to unbounded domains lying in a half space. The functions considered here are either bounded, or have slow decay at infinity. Kelvin inversion is used to obtain another reproducing kernel of Cauchy type, which describes the behaviour of monogenic functions defined over other domains lying in a half space. These domains have the origin on their boundary, and the functions blow up at a specific rate near the origin.
For the entire collection see [Zbl 0881.00038].

##### MSC:
 30G35 Functions of hypercomplex variables and generalized variables 35C15 Integral representations of solutions to PDEs 53C27 Spin and Spin$${}^c$$ geometry
##### Keywords:
Clifford Cauchy kernel; Clifford analysis; Kelvin inversion