标题： 自仿测度在Lalley-Gatzouras地毯上的量化误差的收敛阶 显示英文标题

标题： Convergence order of the quantization error for self-affine measures on Lalley-Gatzouras carpets

摘要： 设$E$是由一组压缩仿射映射$\{f_{ij}\}_{(i,j)\in G}$确定的 Lalley-Gatzouras 窗格。我们研究自仿测度$\mu$在$E$上的量化误差渐进行为。我们证明在精确量化维数下，$\mu$的上界和下界量化系数都远离零和无穷大。这显著推广了之前关于 Bedford-McMullen 窗格上自仿测度量化的工作。新的关键在于对$\mu$量化误差从下界进行估计的方法，以及通过应用 Prohorov 定理构造辅助测度的方法。 显示英文摘要

摘要： Let $E$ be a Lalley-Gatzouras carpet determined by a set of contractive affine mappings $\{f_{ij}\}_{(i,j)\in G}$. We study the asymptotics of quantization error for the self-affine measures $\mu$ on $E$. We prove that the upper and lower quantization coefficient for $\mu$ are both bounded away from zero and infinity in the exact quantization dimension. This significantly generalizes the previous work concerning the quantization for self-affine measures on Bedford-McMullen carpets. The new ingredients lie in the method to bound the quantization error for $\mu$ from below and that to construct auxiliary measures by applying Prohorov's theorem.