Research in Functional Analsys and Mathematical theory of Feynman path integrals.

1.藤原试图给数学严格的治疗费曼路径积分。如果我们巧妙地将Kumanogo的方法与我们1997年发表的工作相结合，似乎有可能得到Kumanogo-Taniguchi定理在电磁场作用下的新证明。藤原撰写的教科书于1999年由东京施普林格出版社出版。标题的英文翻译是“费曼路径积分的数学方法”。2.斯德哥尔摩大学的黑田和Kurasov证明了描述两个算子自伴扩张关系的Krein公式可以理解为两个算子之间的预解方程。讨论了H_∈-微扰理论.水谷研究抛物型非线性偏微分方程的有限元方法. Watanabe和斯德哥尔摩大学的Kurasov一起研究了算子自伴扩张的H_4实现.菅野和仓田的首都大学研究基本解决方案的一致椭圆算子的潜在的一类功能，这是一个推广的一类正多项式。它们成功地证明了它们的基本解，在加权Lp空间和Morrey类中表现出良好的性质.利用这些事实，他们证明了椭圆算子本征值分布的良好估计和本征函数衰减阶的精确信息。

1. Fujiwara tried to give mathematically rigorous treatment of Feynman path integrals. It may seem possible to get a new proof of Kumanogo-Taniguchi theorem for actions with electro-magnetic fields if we cleverly conbine N.Kumanogo's method to that of our work which were published in 1997. Fujiwara wrote a textbook published by Springer Verlarg Tokyo in 1999. The english translation of the title is "Mathematical Method of Feynman path integrals".2. S.T.Kuroda together with P.Kurasov of Stockholm University showed that the Krein's formula describing relations of self-adjoint extension of two operators can be understood as resolvent equation between two operators. And they dicussed H_∈-perturbation theory.3. Mizutani studied finite element methods for parabolic nonlinear partial differential equations.4. Watanabe togeher with Kurasov of Stockholm Univ. studied H_4 realization of selfadjoint extension of operators.5. Sugano together with Kurata of Metropolitan Univ. studied fundamental solutions of uniformly elliptic operators with potentials in a class of functions which is a generalization of the class of positive polynomials. They suceeded in proving their fundamental solutions show good behviour in the weighted L^p space and Morrey classes. Using these facts, they proved a good estimates of distribution of eigen values and sharp information for order of decay of eigen functions of their elliptic operators.