Bounded and almost periodic ultradistributions as boundary values of holomorphic functions

摘要

We represent every bounded ultradistribution of Beurling or of Roumieu type on R as the boundary value of a holomorphic function. In particular, each almost periodic ultradistribution admits such a representation and we characterize the almost periodic ultradistributions that are boundary values of holomorphic functions in the upper (or lower) half-plane in terms of their spectra.