{"title":"From resolvent expansions at zero to long time wave expansions","authors":"T. J. Christiansen, K. Datchev, M. Yang","doi":"arxiv-2408.03234","DOIUrl":null,"url":null,"abstract":"We prove a general abstract theorem deducing wave expansions as time goes to\ninfinity from resolvent expansions as energy goes to zero, under an assumption\nof polynomial boundedness of the resolvent at high energy. We give applications\nto obstacle scattering, to Aharonov--Bohm Hamiltonians, to scattering in a\nsector, and to scattering by a compactly supported potential.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"23 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Spectral Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.03234","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.
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