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High energy bounds on wave operators

Bostelmann, Henning, Cadamuro, Daniela and Lechner, Gandalf 2019. High energy bounds on wave operators. Journal of Operator Theory
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In a general setting of scattering theory, we consider two self-adjoint operators H0 and H1 and investigate the behaviour of their wave operators W±(H1,H0) at asymptotic spectral values of H0 and H1. Specifically, we analyse when ‖(W±(H1,H0)−Pac1Pac0)f(H0)‖<∞, where Pacj is the projector onto the subspace of absolutely continuous spectrum of Hj, and f is an unbounded function (f-boundedness). We provide sufficient criteria both in the case of trace-class perturbations V=H1−H0 and within the general setting of the smooth method of scattering theory, where the high-energy behaviour of the boundary values of the resolvent of H0 plays a major role. In particular, we establish f-boundedness for the perturbed polyharmonic operator and for Schrödinger operators with matrix-valued potentials. Applications of these results include the problem of quantum backflow.

Item Type: Article
Date Type: Completion
Status: Published
Schools: Mathematics
ISSN: 1841-7744
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Date of First Compliant Deposit: 22 August 2020
Date of Acceptance: 22 August 2020
Last Modified: 25 Feb 2021 14:47

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