Wave operators for the linearized Boltzmann equation in one-speed transport theory

A dissipative integro-differential operator $L$ arising in the linearization of Boltzmann's equation in one-speed particle transport theory is considered. Under assumptions ensuring that the point spectrum of $L$ is finite a scalar multiple of the characteristic functions of $L$ is found and a condition for the absence of spectral singularities is indicated. Using the techniques of non-stationary scattering theory and the Sz.-Nagy–Foias functional model direct and inverse wave operators with the completeness property are constructed. The structure of the operator $L$ in the invariant subspace corresponding to its continuous spectrum is studied.