Dispersive estimates for the Schrödinger and Klein–Gordon equations

This is a survey of results on the long-time asymptotic behaviour of solutions of the Schrödinger and Klein–Gordon equations in weighted energy norms. Results obtained from 1975 to 2001 in the spectral scattering theory of Agmon, Jensen–Kato, Jensen–Nenciu, and Murata are described for the Schrödinger equation, along with the author's recent results [1]–[3] obtained jointly with A. I. Komech for the Klein–Gordon equation. The methods used develop the spectral approach as applied to relativistic equations.
Bibliography: 40 titles.