非齐次开集条件下的非齐次自相似测度的量子化
The quantization for in-homogeneous self-similar measures with in-homogeneous open set condition
摘要：
设$(g_i)_{i=1}^M$是一族满足开集条件的压缩相似算子.令$ν$是与$(g_i)_{i=1}^M$相关联的自相似度量。研究了凝聚系统$((f_i)_{i=1}^N,(p_i)_{i=0}^N,ν)$中的非齐次自相似测度$μ$的量子化问题。假设该系统满足一个非齐次开集条件，证明了$r\in(0,\infty)$阶$μ$量子化维数的存在性，并确定了其精确值$ξ_r$ .给出了$ξ_r$维上下量子化系数为正或有限的充分条件。
英文摘要：
Let $(g_i)_{i=1}^M$ be a family of contractive similitudes satisfying the open set condition. Let $ν$ be a self-similar measure associated with $(g_i)_{i=1}^M$. We study the quantization problem for the in-homogeneous self-similar measure $μ$ associated with a condensation system $((f_i)_{i=1}^N,(p_i)_{i=0}^N,ν)$. Assuming a version of in-homogeneous open set condition for this system, we prove the existence of the quantization dimension for $μ$ of order $r\in(0,\infty)$ and determine its exact value $ξ_r$. We give sufficient conditions for the $ξ_r$-dimensional upper and lower quantization coefficient to be positive or finite.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
