{"title":"具有小平移和狄利克特条件的薛定谔算子特征值的渐近性","authors":"D. I. Borisov, D. M. Polyakov","doi":"10.1134/s1064562424702077","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider a non-self-adjoint Schrödinger operator on the unit interval with Dirichlet conditions perturbed by an operator of small translation. The main result is a three-term asymptotic expansion for the eigenvalues with respect to their index, and this asymptotics is uniform in the small translation. We also show that the system of eigenfunctions and generalized eigenfunctions of the considered operators forms a Bari basis in the space of square integrable functions on the considered unit interval.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotics for Eigenvalues of Schrödinger Operator with Small Translation and Dirichlet Condition\",\"authors\":\"D. I. Borisov, D. M. Polyakov\",\"doi\":\"10.1134/s1064562424702077\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>We consider a non-self-adjoint Schrödinger operator on the unit interval with Dirichlet conditions perturbed by an operator of small translation. The main result is a three-term asymptotic expansion for the eigenvalues with respect to their index, and this asymptotics is uniform in the small translation. We also show that the system of eigenfunctions and generalized eigenfunctions of the considered operators forms a Bari basis in the space of square integrable functions on the considered unit interval.</p>\",\"PeriodicalId\":531,\"journal\":{\"name\":\"Doklady Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Doklady Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s1064562424702077\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s1064562424702077","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Asymptotics for Eigenvalues of Schrödinger Operator with Small Translation and Dirichlet Condition
Abstract
We consider a non-self-adjoint Schrödinger operator on the unit interval with Dirichlet conditions perturbed by an operator of small translation. The main result is a three-term asymptotic expansion for the eigenvalues with respect to their index, and this asymptotics is uniform in the small translation. We also show that the system of eigenfunctions and generalized eigenfunctions of the considered operators forms a Bari basis in the space of square integrable functions on the considered unit interval.
期刊介绍:
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.