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Slow uniform distribution
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DOI：10.1007/s11854-026-0433-4.png)
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Abstract
En 中文
We characterize the sequences {nj} of integers for which, for every finite continuous Borel measure mu on [0, 1], the Ces & agrave;ro averages of the sequence {mu<^>(nj)}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{\hat{\mu}(n_{j})\}$$\end{document} converge to 0 (where mu<^>(n)=integral 01exp(-2 pi inx)d mu(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{\mu}(n)=\int_{0}<^>{1}\text{exp}(-2\pi inx)\mathrm{d}\mu(x) $$\end{document} stands for the n-th Fourier-Stieltjes coefficient of mu). Some relevant problems on distribution modulo 1 of real sequences are studied. The slow convergence of functions is introduced and used as a tool. The proof of the equivalence of several definitions of slow convergence utilizes H. P. Rosenthal's combinatorial result.
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SEQUENCES