Previous issue ·  Next issue ·  Recently posted articles ·  Most recent issue · All issues   
Home Overview Authors Editorial Contact Subscribe

Journal of Operator Theory

Volume 76, Issue 2, Fall 2016  pp. 351-385.

Mourre's commutators method for a dissipative form perturbation

Authors:  Julien Royer
Author institution:Institut de Mathematiques de Toulouse, Universite Toulouse 3, Toulouse, 31062, France

Summary: We prove uniform resolvent estimates for an abstract operator given by a dissipative perturbation of a self-adjoint operator in the sense of forms. For this we adapt the commutators method of Mourre. We also obtain the limiting absorption principle and uniform estimates for the derivatives of the resolvent. Finally, we study the absolutely continuous subspace in the sense of Davies. This abstract work is motivated in particular by the Schroedinger and wave equations on a wave guide with dissipation at the boundary.

Keywords: Mourre's theory, limiting absorption principle, dissipative operators, quadratic forms, relatively smooth operators in the sense of Kato

Contents   Full-Text PDF