The upper and lower quantization coefficient for Markov-type measures
Marc Keßeböhmer, Sanguo Zhu · Mathematische Nachrichten · 2017
We study the asymptotic quantization error for Markov-type measures μ on a class of ratio-specified graph directed fractals E. Assuming a separation condition for E, we show that the quantization dimension for μ of order r exists and determine its exact value in terms of spectral radius of a related matrix. We prove that the -dimensional lower quantization coefficient for μ is always positive. Moreover, we establish a necessary and sufficient condition for the -dimensional upper quantization coefficient for μ to be finite.