Much progress has been achieved on linear hyperbolic Cauchy problem, on precise asymptotic behaviors of solutions to nonlinear dissipative and wave equations and on semi-classical resonances, by local and global phase space analysis, in deep coope...

Gunther and Schimming had studied a relation between curvature of Riemannian manifolds and a summation of the trace of the kernel for the heat equation acting to the de Rham complex on manifolds. This summation is one kind of generalization of the...

It has been shown that the resolvent kernel of the free relativistic Schroedinger operator consists of three parts, each of which is different from each other in nature: the fisrt term is the Riesz potential with strong singularity, the second one...

In this project, we are concerned with smoothing properties of solutions to dispersive equations and related topics. Our approach is besed on not only methods of real analysis but also methods of the other areas, especially limiting absorption pri...

Let (V, o) be an isolated singularity with complex dimension n, in a complex euclidean space (C^N/,o). Let M be the intersection of this V and the real hyperspere S^2N-1_E(o), centered at the origin o with radius ε. Then, over M, a CR structure is...

In this project, we are mainly concerned with smoothing properties of solutions to dispersive equations. We used not only methods of real analysis but also methods of the other areas, especially spectral theory. Our subjects are smoothing effect o...

This project is an attempt to make an approach to spectral and scattering theory for relativistic Schrodinger operators. The aim of the project is to investigate the generalized Fourier transforms through analyzing the generalized eigenfunctions i...

1. An analytical proof of the local version of the Gauss-Banner-Chern Theorem has been obtained by Chisato Iwasaki in a paper titled A proof of the Gauss Bonnet-Chern Theorem by the symbolic calculus of pseudo-differential operators, only calculat...