A characterization of the space of Sato-hyperfunctions on the unit circle (Q1096851)

The space \({\mathcal B}(T)\) of Sato hyperfunctions on the unit circle \(T=\{z\in C;| z| =1\}\) is an ib-space, i.e. an inverse limit of b-spaces in the sense of \textit{L. Waelbroeck} [J. Funct. Analysis 1, 409- 418 (1967; Zbl 0201.166)]. The purpose of this paper is to prove the following theorem: The delta function map \(\delta\) :T\(\to {\mathcal B}(T)\) is an ib-space valued analytic map. For any ib-space E and for any ib-space valued analytic map f:T\(\to E\), there exists a unique ib-linear map g:\({\mathcal B}(T)\to E\) such that \(f=g\circ \delta\). The map g is given by an integral with f as a kernel.