On eigenfunction expansions and scattering theory
A systematic approach to expansions in generalized eigenfunctions for self-adjoint operators is presented. An abstract expansion theorem is proven, which allows a unified treatment of different types of eigenfunction expansions known for ordinary differential operators and in the spectral and scattering theory of Schrödinger operators, respectively. Previously this required different approaches. The application of this result to eigenfunction expansions which are related to scattering theory (IP-expansions) is studied in detail. The existence of such expansions is found as a consequence of the existence of wave operators. A very wide scope of scattering systems is treated (2- body or \(N\)-body, short range or long range, Stark effect-, Dirac- and two Hilbert space scattering).
expansions in generalized eigenfunctions for self-adjoint operators
spectral and scattering theory of Schrödinger operators
scientific article; zbMATH DE number 549760
scientific article