Cauchy and Poisson integral representations for ultradistributions of compact support and distributional boundary values

Abstract

SynopsisUltradistributions of compact support are represented as the boundary values of Cauchy and Poisson integrals corresponding to tubular radial domains Tc' =ℝn + iC', C'⊂⊂C, where C is an open, connected, convex cone. The Cauchy integral of is shown to be an analytic function in TC' which satisfies a certain boundedness condition. Analytic functions which satisfy a specified growth condition in TC' have a distributional boundary value which can be used to determine an distribution.