Vektorwertige Distributionen als Randverteilungen holomorpher Funktionen

Abstract

This paper is concerned with the problem, for which locally convex spaces E every E-valued distribution on ℝ is representable by the boundary values of an E-valued holomorphic function on ℂ/ℝ, resp. for which spaces$\frac{\partial }{{\partial \bar z}}f = g$ is solvable in C^∞(ℝ²,E). This is known in the case of (F)-spaces. A complete solution is given in the case of (DF)-spaces. The class of (DF)-spaces, we obtain, turns out to be interesting in a much wider context. This will be contained in a forthcoming paper.