The extension of holomorphic functions on locally convex spaces

全纯函数在局部凸空间上的推广

• 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 /

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.

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在F.More上类型，如果E是核空间，则使用上述结果，他证明了E上的均匀类型的整个功能可以扩展到整个功能f。这是Meise-Vogt的结果的扩展（proc.amer.math.math.math.math.math.math.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.soc.1984）。具有阳性RICCI曲率的非压缩歧管M是微不足道的，并且表明在许多重要情况下，这种猜想是正确的。此外，如果M是具有非负RICCI曲率的完整的非紧密歧管M，他们成功地对N-1同源性组进行了分类。Nishibata（研究人员）研究了双曲线纤维纤维耦合系统和离散的Bolzmann方程。对于这些方程式，他们研究了解决方案的存在和独特性以及在某些条件下的经典解决方案的不存在。

项目成果

Kenji Nishihara and Shinya Nishibata: "Large time behavior of solutions to the Cauchy problem for dimension altheroelastic system with dissipation"Journal of Inequalities and applications. (印刷中).

Kenji Nishihara 和 Shinya Nishibata：“带耗散的维度变弹性系统柯西问题解的大时间行为”不等式与应用杂志（正在出版）。

Tatsuhiro Honda,Mitsuhiro Miyagi,Masaru Nishihara and Mamoru Yoshida: "On continuities of the Borel transforms on the duals of spaces of continuous n-homogeneous polynomials on locally conves spaces"Fukuoka University Science Reports. 30. 1-7 (2000)

Tatsuhiro Honda、Mitsuhiro Miyagi、Masaru Nishihara 和 Mamoru Yoshida：“关于局部凸空间上连续 n 次齐次多项式的空间对偶的 Borel 变换的连续性”福冈大学科学报告。

Shuichi Kawashima and Shinya Nishibata: "Existence of a stationary wave for the discrete Boltzmann equation in the half space"Commum.Math.Phys.. 207. 385-409 (1999)

Shuichi Kawashima 和 Shinya Nishibata：“半空间中离散玻尔兹曼方程的驻波的存在”Commum.Math.Phys.. 207. 385-409 (1999)

Masaru Nishihara: "The extension of polynomials of integral type in locally convex spaces and its application"Proceedings of the Eighth International Colloquium Finite or Infinite Dimensional Complex Analysis(印刷中). 1. 169-174 (2001)

Masaru Nishihara：“局部凸空间中积分型多项式的推广及其应用”第八届国际有限或无限维复分析学术研讨会论文集（出版中）1. 169-174（2001）。

Masaru Nishihara: "On the tensor product representation of polynomials of weak type"Recent Developments in Complex Analysis and Computer Algebra, R.P.Gilbert et al.(eds.), Kluwer Academic Publisher. 1. 259-266 (1999)

Masaru Nishihara：“关于弱类型多项式的张量积表示”，复数分析和计算机代数的最新进展，R.P.Gilbert 等人（编），Kluwer 学术出版社。