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The extension of holomorphic functions on locally convex spaces

全纯函数在局部凸空间上的推广

基本信息

批准号：
11640196
负责人：
NISHIHARA Masaru
金额：
$ 2.37万
依托单位：
Fukuoka Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640196/
关键词：
Entire functions The topological tensor product Nuclear spaces Ricci curvature Homology group Hyperbolic-elliptic coupled systems the discrete Bolzmann equation ボルツマン方程式局所凸空間位相テンソル積表現一様有界型離散型方程式核形空間一様有界型正則写像正則拡大 π-位相 /

项目摘要

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.

设E是复局部凸空间F的闭复线性子空间，则Nishihara（HEAD Escherigator）研究了E上的整函数f何时可以扩展为F上的整函数的问题。首先，通过使用局部凸空间上多项式的拓扑张量积表示，他证明了E上的积分型多项式f可以推广到F上的积分型多项式。此外，如果E是核空间，利用上述结果证明了E上一致有界型的整函数f可以扩张为整函数F，这是Meise-Vogt结果的推广（Proc.Amer.Math.Soc.1984）.Itokawa（GATORS）与Ryouich小林一起研究了一个著名的猜想，即完全非线性空间上的n-1同调群证明了具有正Ricci曲率的紧致流形M是平凡的，并证明了这一猜想在许多重要情况下成立。Nishibata（J. GATORS）研究了双曲-椭圆耦合系统和离散Bolzmann方程。对于这些方程，他们研究了解的存在性和唯一性以及在一定条件下经典解的不存在性。