An aspect for spectral analysis of non-selfadjoint operators : Schrödinger and wave equations

グローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryMRIT 6th Workshop Math-for-Industry Tutorial : Spectral theories of non-Hermitian operators and their applicationWe give an overview for spectral analysis of non-self adjoint operators from a mathematical standpoints. Among other things, we concentrate our considerations on operators that appeared for Schrödinger and wave equations. To these examples, we describe some results of the relation between spectral structure of generator and asymptotic behavior of solutions (energy decay and scattering). Roughly speaking, continuous spectra which are on the real axis effects existence of scattering states (existence of wave and scattering operators) and eigenvalues with negative imaginary part provide total energy decay of solutions