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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