Geometric Aspects of Multiple Fourier Series Convergence on the System of Correctly Counted Sets
作者: Viktor OlevskyiYuliia Olevska
论文集英文名称: Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization
来源数据库: Project Euclid
DOI: 10.7546/giq-19-2019-159-167
原始语种摘要: For multiple Fourier series the convergence of partial sums essentially depends on the type of integer sets, to which the sequence numbers of their terms belong. The problem on the general form of such sets is studying in $u$-convergence theory ($u(K)$ - convergence) for multiple Fourier series. An alternative method of summation is based on the concept of the so-called correctly denumarable sets. In the paper some results describing the $u$-convergence relations and convergence on the system or correctly denumarable sets are presented. It is shown that the system of $U(K)$-sets containing a sphere of infinitely increasing radius for fixed $K$ is correctly denumarable. It is established that for the functions satisfying the Lipschitz condition and having a certain growthing...
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关键词翻译
关键词翻译
  • convergence 汇合
  • correctly 准确地
  • infinitely 无限地
  • system 
  • summation 总和
  • variation 变异
  • multiple 多次的
  • variables 变量
  • ordinary 普通的
  • essentially 本质上