The extension of holomorphic functions on locally convex spaces

点击翻译按钮获取中文摘要

Let E be a closed complex linear subspace of a complex locally convex space F.Then, Nishihara(HEAD INVESTIGATOR)investigated the problem to ask when an entire function f on E can be extended to an entire function on F.Firstly, by using the topological tensor product representation of polynormials on locally convex spaces, he proved that a polynomial f of integral type on E can be extended to a polynomial of integral type on F.Moreover, in case that E is a nuclear space, by using the above result he proved that an entire function f of uniform bounded type on E can be extended to an entire function F.This is an extension of Meise-Vogt' result(Proc.Amer.Math.Soc.1984).Itokawa(INVESTIGATORS)investigated togather with Ryouich Kobayashi a famous conjecture that n-1 homology group on a complete non-compact manifold M with positive Ricci curvature is trivial, and showed that this conjecture is true in a lot of important cases. Moreover they succeeded in classifying n-1 homology group in case that M is a complete non-compact manifold M with non-negative Ricci curvature.Nishibata(INVESTIGATORS)investigated hyperbolic-elliptic coupled systems and the discrete Bolzmann equation. For these equations they investigated the existence and uniqueness of solutions and the non-existence of classical solutions with certain conditions.