Project/Area Number  01302004 
Research Category 
GrantinAid for Cooperative Research (A).

Research Field 
解析学

Research Institution  Okayama University 
Principal Investigator 
SAKATA Hiroshi Okayama University, Faculty of Education Professor, 教育学部, 教授 (60032752)

CoInvestigator(Kenkyūbuntansha) 
境 正一郎 日本大学, 文理学部, 教授 (30130503)
ITO Seizo Kyorin University, Faculty of Social Sciences Professor, 社会科学部, 教授 (40011423)
新屋 均 立命館大学, 理工学部, 教授 (70036416)
OHYA Masanori Science University of Tokyo, Faculty of Science and Technology Professor, 理工学部, 教授 (90112896)
WATARI Chinami Tohoku Gakuin University, Faculty of Arts and Sciences Professor, 教養学部, 教授 (80004274)
INOUE Atsushi FukuokaUniversity, Faculty of Science Professor, 理学部, 教授 (50078557)
MIDORIKAWA Hisaichi Tsuda College, Faculty of Liberal Arts Professor, 学芸学部, 教授 (80055318)

Project Fiscal Year 
1989 – 1990

Project Status 
Completed(Fiscal Year 1990)

Budget Amount *help 
¥14,000,000 (Direct Cost : ¥14,000,000)
Fiscal Year 1990 : ¥6,400,000 (Direct Cost : ¥6,400,000)
Fiscal Year 1989 : ¥7,600,000 (Direct Cost : ¥7,600,000)

Keywords  Functional analysis ; / Real analysis ; / Function spaces ; / Operator algebras ; / Harmonic analysis ; / Representation theory ; / Partial differential equations ; / Function algebras / 函数解析 / 実解析 / 函数空間 / 作用素環 / 調和解析 / 表現論 / 偏微分方程式 / 函数環 
Research Abstract 
1. In the area of real analysis, various results pertaining to harmonic analysis on Euclidean domains were obtained. Among others, a theory of H^P space was developed in detail. A new development of Harmonic analysis was established. The latter was deeply related to differential geometry, partial differential equations and stochastic processes. 2. In the area of applications of function spaces, new aspects of quantum information theory were obtained and applied to irreversible processes. Matrix inequalities in multiport network connections were studied. Various results in the field of evolution equations were obtained and applied to partial differential equations. 3. In the area of representation theory and harmonic analysis, remarkable results were obtained. Discontinuous group in a homogeneous space of reductive type was studied. A construction of infinitedimensional Lie groups was realized. Invariance of dimension of solutions to homogeneous characteristi cequations on semisimple Lie groups was clarified. 4. In the area of functional analysis and partial differential equations, evolution equations, pseudodifferential operators, nonlinear parabolic equations, inverse eigenvalue problems, evolution equations in Hilbert spaces, hyperfunctions and Schrodinger equations were successfully developed. 5. In the area of operator algebras and function algebras, the theory of unbounded derivations in C^*algebras was developed and applied to statistical mechanics. Structure of operator algebras, quantum groups, structure of unbounded operator algebras, and function algebras were analyzed in d etail.
