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We 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 Schrödinge...r 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.続きを見る
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Mendeley出力
