Research in Functional Analsys.

1.藤原试图对费曼路径积分进行严格的数学处理。Fujiwara与K.Taniguchi和N.Kumano-Go利用R^n上的高维振荡积分构造了具有磁势的薛定谔方程的基本解，并给出了高维空间上振荡积分的Kumano-Go-Taniguchi估计的一个新的直接证明。通过对预解式的深入分析，黑田东彦构造了一种称为点相互作用型的奇异势的自伴哈密顿量。推广了他的方法，并成功地通过预解构造了任意的自伴算子。Mizutani和大阪大学的铃木T.Suzuki。证明了有限元数值逼近收敛于退化非线性抛物型方程的真解。他们的方案保持了L^1空间的有序和压缩性质。渡边研究了具有非球对称磁场的薛定谔算子修正散射矩阵的散射相的渐近行为。渡边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半群之差的范数估计。作为应用，他证明了Lie-Trotter乘积公式对半群的一致算子范数收敛。

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.