Smooth perturbations the self–adjoint operators defined by the ℋ︁–2–construction

The existence of the wave operators for the self–adjoint operator constructed by ??_–2–construction is discussed in the abstract theory by using Kato's smooth perturbation method. Moreover, the s–matrix is calculated explicitly.     

Eigenvalues of a λ – Rational Sturm– Liouville Problem

The Sturm – Liouville problem (1.1), (1.2) is considered, which depends rationally on the eigenvalue parameter. Estimates for the eigenvalues and especially for the embedded eigenvalues are proved. Moreover, conditions for the non – existence of embedded eigenvalues are given.     

L∞‐estimates for the Vlasov–Poisson–Fokker–Planck equation

We consider the Vlasov–Poisson–Fokker–Planck equation in three dimensions as the backward Kolmogorov equation associated to a non‐linear diffusion process. In this way we derive new L^∞‐estimates on the spatial density which are uniform in the diffusion parameters. Copyright © 2000 John Wiley & Sons, Ltd.