Canonical sequences of optimal quantization for condensation measures
Doğan Çömez, Mrinal Kanti Roychowdhury · arXiv (Cornell University) · 2017
We consider condensation measures of the form $P:=\frac 13 P\circ S_1^{-1}+ \frac 13 P\circ S_2^{-1}+ \frac 13 ν$ associated with the system $(\mathcal{S}, (\frac 13, \frac 13, \frac 13), ν) , $ where $\mathcal{S}=\{S_i\}_{i=1}^2 $ are contractions and $ ν$ is a Borel probability measure on $\mathbb R$ with compact support. Let $D(μ)$ denote the quantization dimension of a measure $μ$ if it exists. In this paper, we study self-similar measures $ν$ satisfying $D(ν)>κ$, $D(ν)κ$, the $D(P)$-dimensional lower and upper quantization coefficients are finite, positive and unequal; and for $D(ν)\leq κ$, the $D(P)$-dimensional lower quantization coefficient is infinity.