{"title":"weyl极限环情况下耗散schrÖdinger算子的膨胀理论与谱分析","authors":"B. P. Allakhverdiev","doi":"10.1070/IM1991V036N02ABEH002020","DOIUrl":null,"url":null,"abstract":"Dissipative Schrodinger operators are studied in Weyl's limit-circle case. A selfadjoint dilation and a spectral model of these operators are constructed and the characteristic function is computed. Theorems on the completeness of the eigenfunctions of the dissipative operators are proved.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"113 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"39","resultStr":"{\"title\":\"ON DILATION THEORY AND SPECTRAL ANALYSIS OF DISSIPATIVE SCHRÖDINGER OPERATORS IN WEYL'S LIMIT-CIRCLE CASE\",\"authors\":\"B. P. Allakhverdiev\",\"doi\":\"10.1070/IM1991V036N02ABEH002020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Dissipative Schrodinger operators are studied in Weyl's limit-circle case. A selfadjoint dilation and a spectral model of these operators are constructed and the characteristic function is computed. Theorems on the completeness of the eigenfunctions of the dissipative operators are proved.\",\"PeriodicalId\":159459,\"journal\":{\"name\":\"Mathematics of The Ussr-izvestiya\",\"volume\":\"113 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"39\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-izvestiya\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/IM1991V036N02ABEH002020\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-izvestiya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/IM1991V036N02ABEH002020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ON DILATION THEORY AND SPECTRAL ANALYSIS OF DISSIPATIVE SCHRÖDINGER OPERATORS IN WEYL'S LIMIT-CIRCLE CASE
Dissipative Schrodinger operators are studied in Weyl's limit-circle case. A selfadjoint dilation and a spectral model of these operators are constructed and the characteristic function is computed. Theorems on the completeness of the eigenfunctions of the dissipative operators are proved.
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