High Energy Bounds On Wave Operators

Bostelmann H, Cadamuro D, Lechner G (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Journal of Operator Theory Theta Foundation

Book Volume: 86

Pages Range: 61-91

Journal Issue: 1

DOI: 10.7900/jot.2020feb01.2285

Abstract

The wave operators W±(H1, H0) of two selfadjoint operators H0 and H1 are analyzed at asymptotic spectral values. Sufficient conditions for (Formula Presented) are given, where P^ac projects onto the subspace of absolutely continuous spectrum of Hj and f is an unbounded function (f-boundedness), both in the case of trace-class perturbations and in terms of the high-energy behaviour of the boundary values of the resolvent of H0 (smooth method). Examples include f -boundedness for the perturbed polyharmonic operator and for Schrödinger operators with matrix-valued potentials. We discuss an application to the problem of quantum backflow.

Authors with CRIS profile

Gandalf Lechner

Additional Organisation(s)

Lehrstuhl für Mathematik (Operatoralgebren)

Involved external institutions

Cardiff University

United Kingdom (GB) University of York

United Kingdom (GB) Universität Leipzig

Germany (DE)

How to cite

APA:

Bostelmann, H., Cadamuro, D., & Lechner, G. (2021). High Energy Bounds On Wave Operators. Journal of Operator Theory, 86(1), 61-91. https://doi.org/10.7900/jot.2020feb01.2285

MLA:

Bostelmann, Henning, Daniela Cadamuro, and Gandalf Lechner. "High Energy Bounds On Wave Operators." Journal of Operator Theory 86.1 (2021): 61-91.

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