{"title":"Analytic Complexity: Functions with One-Dimensional Stabilizer in the Gauge Group","authors":"V. K. Beloshapka","doi":"10.1134/s0001434624050043","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A differential condition for an analytic function of two variables to have one-dimensional stabilizer in the gauge pseudogroup is obtained. A multiplicative representation (by homogeneous functions) of such functions is given. The stabilizer theorem is improved, and two important examples are constructed. Questions are posed. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"31 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-07-15","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/s0001434624050043","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
A differential condition for an analytic function of two variables to have one-dimensional stabilizer in the gauge pseudogroup is obtained. A multiplicative representation (by homogeneous functions) of such functions is given. The stabilizer theorem is improved, and two important examples are constructed. Questions are posed.
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.
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