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.

DOI: http://dx.doi.org/10.7900/jot.2015dec10.2089
Keywords: Mourre's theory, limiting absorption principle, dissipative operators, quadratic forms, relatively smooth operators in the sense of Kato

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