摘要
We study the quantization for in-homogeneous self-similar measures μ supported on self-similar sets.Assuming the open set condition for the corresponding iterated function system, we prove the existence of the quantization dimension for μ of order r ∈(0, ∞) and determine its exact value ξ_r. Furthermore, we show that,the ξ_r-dimensional lower quantization coefficient for μ is always positive and the upper one can be infinite. A sufficient condition is given to ensure the finiteness of the upper quantization coefficient.
We study the quantization for in-homogeneous self-similar measures μ supported on self-similar sets.Assuming the open set condition for the corresponding iterated function system, we prove the existence of the quantization dimension for μ of order r ∈（0, ∞） and determine its exact value ξ_r. Furthermore, we show that,the ξ_r-dimensional lower quantization coefficient for μ is always positive and the upper one can be infinite. A sufficient condition is given to ensure the finiteness of the upper quantization coefficient.
基金
supported by China Scholarship Council(Grant No.201308320049)
