Project/Area Number  09640215 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  Hokkaido Institute of Technology 
Principal Investigator 
KOSHI Shozo Hokkaido Inst.Tech., Gen.Edu., Professor, 教養部, 教授 (40032792)

CoInvestigator(Kenkyūbuntansha) 
KANETA Takashi Hokkaido Inst.Tech., Gen.Edu., Prof., 教養部, 教授 (50145984)
WAJIMA Masayuki Hokkaido Inst.Tech., Gen.Edu., Prof., 教養部, 教授 (20201163)
KIMURA Nobuyuki Hokkaido Inst.Tech., Gen.Edu., Prof., 教養部, 教授 (10204984)
TAKAHASHI Yuji Hokkaido Univ.of Edu., Prof., 函館校, 教授 (00179540)
YAMAGUCHI Hiroshi Josai Uni., Dept.Science, Prof., 理学部, 教授 (20137798)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,000,000 (Direct Cost : ¥3,000,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1997 : ¥1,700,000 (Direct Cost : ¥1,700,000)

Keywords  hypergroup / F.and M.Riesz theorem / RieszFisher's theorem / ordered topological linear space / generalized supremum / weak Fatou property / Harmonic analysis on group / Riesz space / hyper group / RieszFisher theorem / harmonic analysis on group / F.and M.Ries2 theorem / Rise2 space / ordered topological opaco / Ries2Fisher's theorem / harmanic analysis on group / convex cone / disk hypergroup / F.and M.Riess theorem / ordered linear spaco / topological ordered space / parmonic analysis on group 
Research Abstract 
1. Study on Fourier Analysis (a) We can extend the F.and M.Riesz theorem in the case of hypergroup and nonAbelian compact group. Before, these considerations are made in only Abelian cases. (b) Bochner's theorem says that product of two Riesz sets is also a Riesz set. In the case of loyally compact Abelian group, Bochner's thearem is true by H.Yamaguchi. This time, we can prove that Bochner's theorem is valid in nonAbelian compact group. (c) Fourier Analysis in Disk hypergroup can be developed by many peoples. We can extend these theory in the case of discrete hyper group. 2. Study on Order Structure. (a) Normed linear space with Fatou property is complete (RieszFisher's theorem) is not true in general ordered topological inear space. We find a necessary and sufficient condition tWat the RieszFisher's theorem is valid in the space. (b) We defined generalized suprernum ( or generalized infimum) for a order bounded sub set. We investigate properties of generalized suprem ( or generalized infimum). We construct a theory of generalized supremum and generalized infimum. We find that distributive law is valid if and only if the space is a Riesz space. (c) Optimization theory usually considers only real valued functions. We construct an optimization theory for function whose value is taken in an ordered topological linear space. For application, this theory is very important.
