{"title":"Complex WKB Method (One-Dimensional Linear Problems on the Complex Plane)","authors":"A. A. Fedotov","doi":"10.1134/s0001434623110731","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The survey is devoted to the complex WKB method which arose as an approach to describing the asymptotic behavior of solutions to one-dimensional ordinary differential equations with semiclassical parameter on the complex plane. Later this method was generalized to the case of difference equations. Related constructions arose when studying exponentially small effects in the problem concerning the adiabatic perturbation of the one-dimensional periodic Schrödinger operator. All these three branches of the method are discussed in the survey from a unified position. The main constructions of the method are described and the proofs are either provided or their ideas are described in detail. Some new finds are published for the first time. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0001434623110731","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The survey is devoted to the complex WKB method which arose as an approach to describing the asymptotic behavior of solutions to one-dimensional ordinary differential equations with semiclassical parameter on the complex plane. Later this method was generalized to the case of difference equations. Related constructions arose when studying exponentially small effects in the problem concerning the adiabatic perturbation of the one-dimensional periodic Schrödinger operator. All these three branches of the method are discussed in the survey from a unified position. The main constructions of the method are described and the proofs are either provided or their ideas are described in detail. Some new finds are published for the first time.
期刊介绍：
Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
