From resolvent expansions at zero to long time wave expansions
Analysis of PDEs
2025-05-22 v2 Mathematical Physics
math.MP
Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2408.03234,
title = {From resolvent expansions at zero to long time wave expansions},
author = {T. J. Christiansen and K. Datchev and M. Yang},
journal= {arXiv preprint arXiv:2408.03234},
year = {2025}
}
Comments
v2: 14 pages, 1 figure. Updated following referees' comments