CLIFFORD ANALYSIS OVER UNBOUNDED-DOMAINS

A modified Cauchy kernel is introduced over unbounded domains whose co mplement contains nonempty open sets. Basic results on Clifford analys is over bounded domains are now carried over to this more general cont ext and to functions that are no longer assumed to be bounded. In part icular Plemelj formulae are explicitly computed, Basic properties of t he Cauchy transform over unbounded domains lying in a half space are i nvestigated, and an orthogonal decomposition of the L-2 space for such a domain is set up. At the end a boundary value problem will be studi ed in the case of an unbounded domain without using weighted Sobolev s paces. (C) 1997 Academic Press.