From resolvent expansions at zero to long time wave expansions

We prove a general abstract theorem deducing wave expansions as time goes to infinity from resolvent expansions as energy goes to zero, under an assumption of polynomial boundedness of the resolvent at high energy. We give applications to obstacle scattering, to Aharonov--Bohm Hamiltonians, to scatt...

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Bibliographic Details
Published in:arXiv.org 2024-12
Main Authors: Christiansen, T J, Datchev, K, Yang, M
Format: Article
Language:English
Subjects:
Polynomials
Scattering
Online Access:Get full text
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Summary:We prove a general abstract theorem deducing wave expansions as time goes to infinity from resolvent expansions as energy goes to zero, under an assumption of polynomial boundedness of the resolvent at high energy. We give applications to obstacle scattering, to Aharonov--Bohm Hamiltonians, to scattering in a sector, and to scattering by a compactly supported potential.
ISSN:2331-8422