RESEARCH ON FUNCTIONAL ANALYSIS

推广了F.和M.Riesz定理，发现局部紧Abelian群的结构依赖于该群上的解析测度的性质.得到了Hardy空间定理与Douglas代数定理的关系。(S.KOSHI，Yuji Takahashi，K.IZUCHI)绝对和算子与Banach空间中可补子空间的存在性有关。研究了Hilbert空间中算子的(Yasuji Takahashi)序结构，得到了这种情况下的Lebesque分解定理。在对称空间上的热方程中，解决了最后温度分布是否存在的问题。(K.OKAMOTO)其他结果：Riemann曲面、Mobius函数、序空间上的凸算子和路径积分是我们的研究对象。(N.Komuro，M.Hatashi，C.NARA，T.Ichinose，A.Arai，H.Yamaguchi)

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)