Research in Functional Analsys.

1. 藤原试图给出费曼路径积分的严格数学处理方法。他和Tsuchida一起构造了具有磁势的薛定谔方程的基本解，使用了R^n上的大维n的振荡积分。Fujiwara与K.Taniguchi和n.a umano- taniguchi对大维空间上的振荡积分的估计给出了一个新的直接证明。S.T.Kuroda通过对解的深入分析，构造了具有非常奇异势的点相互作用型的自伴随哈密顿算子。他推广了他的方法，并成功地通过解析构造了任意自伴随算子。Mizutani和大阪大学的T.Suzuki一起证明了退化非线性抛物方程的有限元数值近似收敛的真解。它们的格式保持了L^1空间中的有序性和收缩性。Watanabe研究了无球对称磁场下Schr6dinger算子修正散射矩阵的散射相位渐近行为。Watanabe还研究了具有光滑势和奇异势的薛定谔算子的谱集中和共振。Ichinose成功地证明了Kac转移算子与Schr6dinger半群之间差异的范数估计。作为应用，证明了Lie-Trotter乘积公式的一致算子范数收敛性。

1. Fujiwara tried to give mathematically rigorous treatment of Feynman path integrals. He together with Tsuchida constructed the fundamental solution of Schrodinger equation with magnetic potentials, using oscillatory integrals over R^n with large dimension n. Fujiwara, together with K.Taniguchi and N.Kumano-go, gave a new and direct proof of Kumano-go-Taniguchi estimate for oscillatory integral over a large dimensional space.2. S.T.Kuroda constructed self adjoint Hamiltonians with a very singular potential called point interaction type through deep analysis of resolvents. He generalized his method and succeeded in constructing any self adjoint operators through resolvents.3. Mizutani together with T.Suzuki of Osaka Univ. proved a finite element numerical approximation converges La the true solution of degenerating nonlinear parabolic equations. Their scheme preserves order and contraction property in L^1 space.4. Watanabe studied asymptotic behavior of scattering phase for modified scattering matrfx of Schr6dinger operators with magnetic field without spherical symmetry. Watanabe also studied spectral concentration and resonaces for Schr6dinger operators having smooth potential or potential with singularity.5. Ichinose succeeded in proving norm estimate for the difference between Kac's transfer operator and Schr6dinger semi-group. As an application he proved the uniform operator norm convergence of Lie-Trotter product formula to the semi-group.