Fourier transforms in spaces of hyperfunctions and Hartogs' type phenomena (Q2759783)

This paper reports on some applications of the theory of the local Fourier transform for hyperfunctions and the related duality theory for the space \(B/A\), where \(B\) is the space of germs of hyperfunctions at \(0 \in \mathbb{R}^{n}\) and \(A\) is the subspace of real-analytic functions in \(B\). Some results on the existence of boundary traces for one-sided solutions of linear partial pseudodifferential equations in the \(C^{\infty}\) case and the analytic case are given. Then, Hartogs type phenomena for hyperfunctions with holomorphic parameters are described. The proofs of these results are not given here.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00056].