{"title":"具有快速振荡复值势的Schrödinger算子的本质m-扇形和本质谱","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":"{\"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}","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}
Essential m-sectoriality and essential spectrum of the Schrödinger operators with rapidly oscillating complex-valued potentials
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.