Reproducing bergman kernels in clifford analysis

Abstract

It is proved that the module of Clifford-algebra-valued square-integrable eigenfunctions of the Dirac-operator in an open subset Ω of R ^m is a Hilbert-module with reproducing kernel; this reproducing kernel for the case where Ω is the unit ball or the Euclidean space itself, is explicitly constructed. Also the module of square-integrable polymonogenic functions in R ^m is studied. It turns out that it is a Hilbert-module with reproducing kernel too.

AMS No:

• 30035
• 46E20

^∗Research associate supported by N.F.W.O., Belgium.

^∗Research associate supported by N.F.W.O., Belgium.

Notes

^∗Research associate supported by N.F.W.O., Belgium.