TAJIMA Shinichi Niigata University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (70155076)
KAWAMURA Shinzo Yamagata University, Faculty of Science, Professor, 理学部, 教授 (50007176)
SANO Shigeru Polytechnic University, Department of Liberal Arts & Sciences, Professor, 基礎学科, 教授
SATO Ryotaro Okayama University, Faculty of Science, Professor, 理学部, 教授 (50077913)
Recent progress in the fields of Functional and Real Analysis has been traced, and we tried to synthesize many different results for the future development. We had 5 groups, that is, "real analysis", "quantum mathematics and operator theory", "representation theory and harmonic analysis", "operator algebra" and "functional analytic research of partial differential equations". Each group organized several seminars every year. As the whole, we organized a joint symposium and three times meetings every year so as to direct for the future research. The joint symposiums were held in Toho university on July 15-17 in 1998, in Ibaragi University on July 22-24 in 1997.
As an example, we mention the works on quantum information theory and complexity done by the group of quantum mathematics and operator theory. A synthesis of the dynamics of system and the complexity was studied under the name of information dynamics. In information dynamics we need many fundamental results in functional and real analysis such as operator algebras, differential equation, harmonic analysis, ergodic theory, where individual research are indispensable.