Asymptotic order of the quantization error for a class of self-similar
measures with overlaps
Asymptotic order of the quantization error for a class of self-similar
measures with overlaps
Let $\{f_i\}_{i=1}^N$ be a set of equi-contractive similitudes on $\mathbb{R}^1$ satisfying the finite-type condition. We study the asymptotic quantization error for self-similar measures $\mu$ associated with $\{f_i\}_{i=1}^N$ and a positive probability vector. With a verifiable assumption, we prove that the upper and lower quantization coefficient for $\mu$ are both bounded …