Dirichlet 数列的切比雪夫子空间

IF 0.2 Q4 MATHEMATICS

Moscow University Mathematics Bulletin Pub Date : 2023-12-01 DOI:10.3103/s0027132223060037

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引用次数: 0

摘要

摘要哈尔和科尔莫戈罗夫发现了任意紧凑集上连续函数空间中的有限维子空间是切比雪夫子空间的必要条件和充分条件。本文证明了在区间 \((0,\infty)\)中的连续有界函数的 \(\mathbf{C}(0,\infty]\) 空间中，在无穷远处有一个极限的 Dirichlet 级数的子空间构成切比雪夫子空间。

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Chebyshev Subspaces of Dirichlet Series

Abstract

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.

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来源期刊

Moscow University Mathematics Bulletin MATHEMATICS-

CiteScore

0.60

自引率

25.00%

发文量

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.