Project/Area Number  09640173 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  SHINSHU UNIVERSITY 
Principal Investigator 
KAWABE Jun Shinshu University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (50186136)

CoInvestigator(Kenkyūbuntansha) 
TAKANO Kazuhiko Shinshu University, Faculty of Engineering, Lecturer, 工学部, 講師 (80252063)
YAMASAKI Motohiro Shinshu University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30021017)
KIMURA Morishige Shinshu University, Faculty of Engineering, Professor, 工学部, 教授 (00026345)
SAKAI Yuji Shinshu University, Faculty of Engineering, Professor, 工学部, 教授 (80021004)
OKUYAMA Yasuo Shinshu University, Faculty of Engineering, Professor, 工学部, 教授 (70020980)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥1,800,000 (Direct Cost : ¥1,800,000)
Fiscal Year 1998 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1997 : ¥1,000,000 (Direct Cost : ¥1,000,000)

Keywords  tensor product of vector measures / weak convergence of vector measures / fuzzy optimal control / Norlund summability / rearrangement of vectorvalued functions / digital control of continuoustime linear systems / martingale / Kahlerian submersion / ベクトル測度のテンソル積 / ベクトル測度の弱収束 / ファジィ制御 / ネェールンド総和法 / ベクトル値関数の並べかえの理論 / 連続線形系のディジタル制御 / マルチンゲール / ケーラー沈み込み / フーリエ級数 / ネェルンド総和法 / マルチンゲル 
Research Abstract 
We have studied weak convergence of vector measures with values in Banach spaces and nuclear spaces, and have applied it to several interesting problems in real analysis, probability theory, control theory and so on. Some of our important results are as follows : 1. We proved that the weak convergence of a net of tensor products of vector measures with values in nuclear spaces follows from that of the corresponding net of real product measures. 2. We gave weak (sequential) compactness criteria for Radon vector measures with values in several locally convex spaces. Consequently, our result contains previous criteria obtained by ProkhorovLeCam for real measures and by Marz and Shortt for Banach space valued measures. 3. We extended a type of Strassen's theorem for probability measures to positive vector measures with values in the weak dual of a barreled locally convex space which has certain order conditions. 4. We examined the convergence of feedback laws constructed by Mamdani method and the convergence of solutions of a nonlinear state equation in fuzzy control system. As an application, we ensured the existence of fuzzy optimal control. 5. We proved a theorem on the generalized Norlund summability (N, pn, qn) of Legendre series, which contains previous results by V.Singh, N.P.Mishra and Ajit Singh. It is also an Legendre analogue of a result due to Rajagopal. 6. We proved some theorems on the generalized Norlund summability (N, pn, qn) of Fourier series and its conjugate series, which contain several previous results by A.N.Singh and S.P.Khare.
