Mourre's method for a dissipative form perturbation

Julien Royer (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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. This abstract work is motivated by the Schrödinger and wave equations on a wave guide with dissipation at the boundary.

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Julien Royer. Mourre's method for a dissipative form perturbation. Journal of Operator Theory, 2016, 16 (2). ⟨hal-01088162⟩