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Reproducing Kernels and Conformal Mappings in Rn

✍ Scribed by J Cnops

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
176 KB
Volume
220
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper we look at the theory of reproducing kernels for spaces of functions in a Clifford algebra ‫ޒ‬ . A first result is that reproducing kernels of this kind are 0, n solutions to a minimum problem, which is a non-trivial extension of the analogous property for real and complex valued functions. In the next sections we restrict our attention to Szego and Bergman modules of monogenic functions. The transforma-ẗion property of the Szego kernel under conformal transformations is proved, and ẗhe Szego and Bergman kernels for the half space are calculated.

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