Elements of \({\mathcal D}_{L^s}^{\prime (M_ p)}\) and \({\mathcal D}_{L^s}^{\prime (M_ p)}\) as boundary values of holomorphic functions (Q1125846)

The author deals with holomorphic function spaces whose elements have boundary values in spaces of distributions, ultradistributions, and infra-hyperfunctions and, conversely, with the boundary value representation of elements in the quoted generalized function spaces by holomorphic functions. By using a simple and powerful method based on almost analytic extension and Stokes' theorem as well as on Komatsu's method, the complete boundary value characterization for spaces of ultradistributions related to a non-quasianalytic sequence is put into evidence in the frame of three theorems based on five lemmas.