莫朗集上加倍测度量子误差的渐近均匀性

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莫朗集上加倍测度量子误差的渐近均匀性朱三国江苏理工学院数理学院常州 213001 The Asymptotic Uniformity of the Quantization Error for Doubling Measures on Moran Sets San Guo ZHUSchool of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, P. R. China

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摘要我们研究了莫朗集E上的加倍概率测度μ的量子误差的渐近性质.对μ的任一r阶n-最优集α_n及α_n对应的任一Voronoi分划{P_a（α_n）}_{a∈α_n}，定义I_a（α_n，μ）=∫_{P_a（α_n）}d（x，a）^rdμ（x）；J（α_n，μ）：=min_{a∈α_n}I_a（α_n，μ），J（α_n，μ）：=max_{a∈α_n}I_a（α_n，μ）.记e_n，r（μ）为测度μ的r阶n-级量子误差.在一定意义的开集条件下，我们对加倍测度μ证明了Gersho猜测的下述弱形式：J（α_n，μ），J（α_n，μ）?1/ne_n,rr（μ）.

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收稿日期: 2020-05-19

MR (2010):

O174.1

基金资助:国家自然科学基金资助项目（11571144）

作者简介: 朱三国,E-mail:sgzhu@jsut.edu.cn

引用本文:

朱三国. 莫朗集上加倍测度量子误差的渐近均匀性[J]. 数学学报, 2021, 64(5): 821-838. San Guo ZHU. The Asymptotic Uniformity of the Quantization Error for Doubling Measures on Moran Sets. Acta Mathematica Sinica, Chinese Series, 2021, 64(5): 821-838.

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