On the scattering theory and the singular perturbations for the self-adjoint operators

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1. The H-2-construction to treat the singular perturbation for the self-adjoint operator by the operator theoretical method has been studied by K. Watanabe. The author obtains some results for the operator, for example, necessary and sufficient condition of the existence of embedded eigenvalues, representation of the scattering matrix and etc.2. The regularity of the solutions for the Maxwell, Stokes and Navier-Stokes equation with the interface has been investigated by K. Watanabe. Especially the following results is remarkable : if the tangential component does not have the singularity, then the regularity of the solution gains rank one.3. The partial differential equation with the dissipative term has been studied by K. Watanabe. The relationship of this spectrum type and the behavior of the time decay of the solutions has been studied.4. Krein's formula (which is a generalization of the second resolvent equation) was studied by S.T. Kuroda and published5. The finite elements method for the bi-harmonic Dirichlet problems on the polygon in the plane (not necessary convex) has been studied by A. Mizutani.6. The behaviors of the solution at the time infinity for the system of the nonlineat partial differential equations (for example, the coupled Schrodinger and Klein-Goldon) have been studied by A. Shimura and published.7. The regularity and the uniqueness for the initial date problems of the Euler equation have been studied by T. Ogawa and published.8. The scattering theory for the dissipative system has been studied by M. Kadowaki and published.