{"title":"某些部分周期系数算子的特征值不存在","authors":"N. Filonov","doi":"10.1090/spmj/1730","DOIUrl":null,"url":null,"abstract":"<p>The absence of eigenvalues is proved for the Schrödinger operator <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"negative normal upper Delta plus upper V left-parenthesis x comma y right-parenthesis\">\n <mml:semantics>\n <mml:mrow>\n <mml:mo>−<!-- − --></mml:mo>\n <mml:mi mathvariant=\"normal\">Δ<!-- Δ --></mml:mi>\n <mml:mo>+</mml:mo>\n <mml:mi>V</mml:mi>\n <mml:mo stretchy=\"false\">(</mml:mo>\n <mml:mi>x</mml:mi>\n <mml:mo>,</mml:mo>\n <mml:mi>y</mml:mi>\n <mml:mo stretchy=\"false\">)</mml:mo>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">-\\Delta + V(x,y)</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> in the Euclidean space whose potential is periodic in some variables and decays in the remaining variables faster than power <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"1\">\n <mml:semantics>\n <mml:mn>1</mml:mn>\n <mml:annotation encoding=\"application/x-tex\">1</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>. A similar result for the Maxwell operator is established.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The absence of eigenvalues for certain operators with partially periodic coefficients\",\"authors\":\"N. Filonov\",\"doi\":\"10.1090/spmj/1730\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The absence of eigenvalues is proved for the Schrödinger operator <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"negative normal upper Delta plus upper V left-parenthesis x comma y right-parenthesis\\\">\\n <mml:semantics>\\n <mml:mrow>\\n <mml:mo>−<!-- − --></mml:mo>\\n <mml:mi mathvariant=\\\"normal\\\">Δ<!-- Δ --></mml:mi>\\n <mml:mo>+</mml:mo>\\n <mml:mi>V</mml:mi>\\n <mml:mo stretchy=\\\"false\\\">(</mml:mo>\\n <mml:mi>x</mml:mi>\\n <mml:mo>,</mml:mo>\\n <mml:mi>y</mml:mi>\\n <mml:mo stretchy=\\\"false\\\">)</mml:mo>\\n </mml:mrow>\\n <mml:annotation encoding=\\\"application/x-tex\\\">-\\\\Delta + V(x,y)</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> in the Euclidean space whose potential is periodic in some variables and decays in the remaining variables faster than power <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"1\\\">\\n <mml:semantics>\\n <mml:mn>1</mml:mn>\\n <mml:annotation encoding=\\\"application/x-tex\\\">1</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>. A similar result for the Maxwell operator is established.</p>\",\"PeriodicalId\":51162,\"journal\":{\"name\":\"St Petersburg Mathematical Journal\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-08-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"St Petersburg Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/spmj/1730\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1730","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
The absence of eigenvalues for certain operators with partially periodic coefficients
The absence of eigenvalues is proved for the Schrödinger operator −Δ+V(x,y)-\Delta + V(x,y) in the Euclidean space whose potential is periodic in some variables and decays in the remaining variables faster than power 11. A similar result for the Maxwell operator is established.
期刊介绍：
This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.
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