{"title":"Essential m-sectoriality and essential spectrum of the Schrödinger operators with rapidly oscillating complex-valued potentials","authors":"Y. Oshime","doi":"10.21099/TKBJM/1461270057","DOIUrl":null,"url":null,"abstract":"Schrödinger operators T0 1⁄4 sþ qðxÞ with rapidly oscillating complex-valued potentials qðxÞ are considered. Each of such operators is sectorial and hence has Friedrichs extension. We prove that T0 is essentially m-sectorial in the sense that the closure of T0 coincides with its Friedrichs extension T . In particular, T0 is essentially self-adjoint if the rapidly oscillating potential qðxÞ is realvalued. Further, we prove sessðTÞ 1⁄4 1⁄20;yÞ under somewhat stricter condition on the potentials qðxÞ.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.21099/TKBJM/1461270057","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsukuba Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21099/TKBJM/1461270057","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Schrödinger operators T0 1⁄4 sþ qðxÞ with rapidly oscillating complex-valued potentials qðxÞ are considered. Each of such operators is sectorial and hence has Friedrichs extension. We prove that T0 is essentially m-sectorial in the sense that the closure of T0 coincides with its Friedrichs extension T . In particular, T0 is essentially self-adjoint if the rapidly oscillating potential qðxÞ is realvalued. Further, we prove sessðTÞ 1⁄4 1⁄20;yÞ under somewhat stricter condition on the potentials qðxÞ.