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Asymptotic order of the quantization errors for a class of self-affine measures

朱三国 教授(江苏理工大学数理学院)
Monday, January 1st, 2018, 9:30 AM  华东师范大学

摘要:Let $E$ be a Bedford-McMullen carpet determined by a set of affine mappings $(f_{ij})_{(i,j)\in G}$ and $\mu$ a self-affine measure on $E$ associated with a probability vector $(p_{ij})_{(i,j)\in G}$. We prove that, for every $r\in(0,\infty)$, the upper and lower quantization coefficient are always positive and finite in its exact quantization dimension $s_r$. As a consequence, the $n$th quantization error for $\mu$ of order $r$ is of the same order as $n^{-\frac{1}{s_r}}$. In sharp contrast to the Hausdorff measure for Bedford-McMullen carpets, our result is independent of the horizontal fibres of the carpets.


在Math.Z、Science China Math.、Nonlinearity、Proc. Amer. Math. Soc.、J. Number Theory等国内外知名SCI源刊发表论文23篇。

邀请人: 李文侠 教授
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