RESEARCH ON FUNCTIONAL ANALYSIS

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GENERALIZATION OF F. AND M. RIESZ THEOREN IS OBTAINED AND IT IS FOUND THAT THE STRUCTURE OF A LOCALLY COMPACT ABELIAN GROUP DEPENDS ON THE PROPERTIES OF MEASURES OF ANALYTIC ON THE GROUP. RELATIONS OF HARDY SPACE THEOPY AND DOUGLAS ALGEBRA'S THEOREM ARE OBTAINED. (S.KOSHI, YUJI TAKAHASHI, K.IZUCHI)ABSOLUTELY SUMMING OPERATORS ARE RELATED TO THE EXISTENCE OF COMPLEMENTED SUBSPACES IN BANACH SPACES. (YASUJI TAKAHASHI)ORDER STRUCTURES IN OPERATORS OF HILBERT SPACES ARE CONSIDERED AND THE LEBESQUE DECOMPOSITION THEOREM IN THIS CASE IS OBTAINED. (T.ANDO)IN HEAT EQUATIONS ON SYMMETRIC SPACES, A QUESTION WHETHER LAST TEMPARATURE DISTRIBUTION EXISTS OR NOT IS SOLVED. (K.OKAMOTO)OTHER RESULTS : RIEMANN SURFACES, MOBIUS FUNCTIONS, CONVEX OPERATORS ON ORDERED SPACE, AND PATH INTEGRALS ARE OBJECTS OF OUR RESEARCH. (N. KOMURO, M. HATASHI, C. NARA, T. ICHINOSE, A. ARAI, H. YAMAGUCHI)