无界情况下Vilenkin系统傅里叶级数一致收敛的性质 $$\boldsymbol{p}_{\boldsymbol{k}}$$

IF 0.2 Q4 MATHEMATICS

Moscow University Mathematics Bulletin Pub Date : 2023-01-10 DOI:10.3103/s0027132222050084

S. M. Voronov

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引用次数: 0

摘要

摘要研究了关于零维紧交换群的字符系统的级数。推广了具有广义有界$\Phi$ -涨落的函数在无界拟单调$p_{k}$情况下的Vilenkin系统的傅里叶级数收敛性检验，证明了先前在有界序列${p_{k}}$情况下得到的结论。

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On the Attribute of Uniform Convergence of Fourier Series of the Vilenkin System in the Case of Unbounded $$\boldsymbol{p}_{\boldsymbol{k}}$$

Abstract

Series with respect to a system of characters of a zero-dimensional compact commutative group are considered. Generalization of the test of convergence of Fourier series of the Vilenkin system in the case of unbounded quasimonotone $p_{k}$ for functions having a generalized bounded $\Phi$-fluctuation, which was earlier obtained in the case of bounded sequences ${p_{k}}$, is proved.

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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.