arXiv subjects
Publications and source records attributed to Kohei Umeta.
The paper studies several properties of Laplace hyperfunctions introduced by H.~Komatsu in the one dimensional case and by the authors in the higher dimensional cases from the viewpoint of \v{C}ech-Dolbeault cohomology theory, which enables us, for example, to construct the Laplace transformation and its inverse in a simple way. We also give some applications to a system of PDEs with constant coefficients.
We construct a framework which gives intuitive representation of local cohomology groups. By defining the concrete mappings among them, we show their equivalence. As an application, we justify intuitive representation of Laplace hyperfunctions.
We establish an edge of the wedge theorem for the sheaf of holomorphic functions with exponential growth at infinity and construct the sheaf of Laplace hyperfunctions in several variables. We also study the fundamental properties of the sheaf of Laplace hyperfunctions.