関数解析的手法による位相力学系の研究

使用泛函分析方法研究拓扑动力系统

• 批准号: 09640149
• 负责人: KAWAMURA Shinzo
• 金额: $ 1.92万
• 依托单位: YAMAGATA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640149/
• 关键词: topological dynamics; chaotic dynamics; wavelets theory; operator algebras; transformation group; operator theory; meromorphic maps; multiplier; ウェブレット理論; 作用素論; コンパクトアーベル群; ウェヴレット理論; モリー空間; 超越的有理写像; モリ-空間

(1) S. Kawamura who is the head investigator organized two workshops in UNCC and Yamagata University in the beginning and the end of 1999 respectively. Moreover he studied chaotic maps on metric measure space. As a way of studying he used the theory of operator algebras and obtained some important results concerning chaos maps and wavelets theory.(2) J. Tomiyama has clarified the structure of bounded orbit equivalence of topological dynamical systems for the interplay between topolocicl dynamics and C*-theory. He also classified the ideals of homeomorphism C*-algebras to show their structure in connection with the general isomorphism problem.(3) F. Uchida showed behavior of smooth actions of non-compact semi-simple Lie groups. Moreover he clarified construction and classification concerning smooth actions of Sp(p,q) on the (4p+4q-1)-sphere.(4) T. Okayasu obtained some important results concerning Lowener-Hainz inequalties in Banach*-algebras and a multivariable von Neumann's inequality.(5) S. Mori proved, for any given transcendental meromorphic mapping of CィイD1mィエD1 into PィイD1nィエD1(C), that one can eliminate all defects (deficient hyperplanes, deficient hypersurfaces) and defects of rational moving targets by a small deformation of the mapping, and also proved that meromorphic mappings without defects in dense in a space of transcendental meromorphic mappings.(6) E. Sato studied the Banach algebra M(p,q), which is defined by the translation invariant operators from Lp(G) to Lq(G) on infinite compact abelian groups. Also I studied the transference of continuity from maximal Fourier multiplier operators on n-dimensional Euclidian space to those on n-dimensional torus.

(1)首席调查员S.Kawamura分别于1999年初和年底在赔偿委员会和山形大学组织了两次讲习班。此外，他还研究了度量度量空间上的混沌映射。作为一种研究方法，他利用算子代数理论，得到了关于混沌映射和小波理论的一些重要结果。(2)J.Tomiyama阐明了拓扑动力系统的有界轨道等价结构，用于拓扑动力学和C*-理论的相互作用。他还结合一般的同构问题对同胚C*-代数的理想进行了分类，以显示其结构。(3)内田证明了非紧半单李群的光滑行为。(4)T.Okayasu得到了关于Banach*-代数中的Lowener-Hainz不等式和一个多元von Neumann不等式的一些重要结果.(5)S.Mori证明了对于任何给定的从CィイD_1mィエD_1到P_ィイD_1nィエD_1(C)的超越亚纯映射，人们可以通过该映射的小变形来消除所有的缺陷(亏超平面，亏超曲面)和有理运动目标的缺陷，(6)E.Sato研究了由无限紧交换群上的Lp(G)到Lq(G)的平移不变算子定义的Banach代数M(p，q)。并研究了n维欧氏空间上的极大傅立叶乘子算子到n维环面上的极大傅立叶乘子算子的连续性问题。

项目成果

S.Kawamura: "Chaotic maps on metric measure spaces and behavior of states"京大数理解析研究所講究録に発表予定. (未定).

S. Kawamura：“关于度量测量空间和状态行为的混沌图” 预定在京都大学数学科学研究所的 Kokyuroku 上发表（待定）。

F.Uchida: "On smooth SUo(P、q)-actions on S^<P+q-1>,II" Tohoku Math.J.49・2. 185-202 (1997)

F.Uchida：“关于 S^<P+q-1>,II 上的平滑 SUo(P, q)-作用”Tohoku Math.J.49・2 (1997)。

J. Tomiyama: "Structure of ideals and isomorphism problems of C*-crossed products by single homeomorphisms"Tokyo Jour. Math.. (To appear).

J. Tomiyama：“单同胚的 C* 交叉产物的理想结构和同构问题”《东京杂志》。

S. Mori: "Elimination of defects of meromorphic mappings of CィイD2mィエD2 into PィイD2nィエD2(C)"Annales Academic Scientiarum Fennicae Mathematica. 24. 89-104 (1999)

S. Mori：“消除 C2D2D2 亚态映射到 P2D2D2(C) 的缺陷”Annales Academic Sc​​ientiarum Fennicae Mathematica 24. 89-104 (1999)。

S. Mori: "Elimination of defects of meromorphic mappings by small deformation"Recent Developments of Complex Analysis and computer Algebra, Kluwer Academic Publishers. 247-258 (1999)

S. Mori：“通过小变形消除亚纯映射的缺陷”，复分析和计算机代数的最新发展，Kluwer 学术出版社。