{"title":"Dirichlet 数列的切比雪夫子空间","authors":"","doi":"10.3103/s0027132223060037","DOIUrl":null,"url":null,"abstract":"<span> <h3>Abstract</h3> <p>Haar and Kolmogorov found the necessary and sufficient conditions under which finite-dimensional subspaces in the space of continuous functions on an arbitrary compact set are Chebyshev. In this paper, it is proved that subspaces of Dirichlet series form Chebyshev subspaces in the space of <span> <span>\\(\\mathbf{C}(0,\\infty]\\)</span> </span> of continuous and bounded functions in the interval <span> <span>\\((0,\\infty)\\)</span> </span> that have a limit at infinity.</p> </span>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.2000,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Chebyshev Subspaces of Dirichlet Series\",\"authors\":\"\",\"doi\":\"10.3103/s0027132223060037\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<span> <h3>Abstract</h3> <p>Haar and Kolmogorov found the necessary and sufficient conditions under which finite-dimensional subspaces in the space of continuous functions on an arbitrary compact set are Chebyshev. In this paper, it is proved that subspaces of Dirichlet series form Chebyshev subspaces in the space of <span> <span>\\\\(\\\\mathbf{C}(0,\\\\infty]\\\\)</span> </span> of continuous and bounded functions in the interval <span> <span>\\\\((0,\\\\infty)\\\\)</span> </span> that have a limit at infinity.</p> </span>\",\"PeriodicalId\":42963,\"journal\":{\"name\":\"Moscow University Mathematics Bulletin\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2023-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Moscow University Mathematics Bulletin\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3103/s0027132223060037\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow University Mathematics Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s0027132223060037","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Haar and Kolmogorov found the necessary and sufficient conditions under which finite-dimensional subspaces in the space of continuous functions on an arbitrary compact set are Chebyshev. In this paper, it is proved that subspaces of Dirichlet series form Chebyshev subspaces in the space of \(\mathbf{C}(0,\infty]\) of continuous and bounded functions in the interval \((0,\infty)\) that have a limit at infinity.
期刊介绍：
Moscow University Mathematics Bulletin is the journal of scientific publications reflecting the most important areas of mathematical studies at Lomonosov Moscow State University. The journal covers research in theory of functions, functional analysis, algebra, geometry, topology, ordinary and partial differential equations, probability theory, stochastic processes, mathematical statistics, optimal control, number theory, mathematical logic, theory of algorithms, discrete mathematics and computational mathematics.
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