Mourre's commutators method for a dissipative form perturbation (Q2835265)

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scientific article; zbMATH DE number 6658808
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Mourre's commutators method for a dissipative form perturbation
scientific article; zbMATH DE number 6658808

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    Mourre's commutators method for a dissipative form perturbation (English)
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    1 December 2016
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    Mourre's theory
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    limiting absorption principle
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    dissipative operators
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    quadratic forms
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    relatively smooth operators in the sense of Kato
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    By using a generalization of the commutators method of Mourre, the author proves uniform resolvent estimates, the limiting absorption principle and estimates for the derivatives of the resolvent for a dissipative operator given by a form-perturbation of a self-adjoint operator. The absolutely continuous subspace in the sense of Davies is also investigated. Some applications of this study for the Schrödinger operator on a wave-guide or on a half-space with dissipation at the boundary, and for the Schrödinger operator on \(\mathbb{R}^d\) whose absorption index is singular for low frequencies, are also presented.
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