Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures

Mrinal Kanti Roychowdhury. "Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures." Bulletin of the Polish Academy of Sciences. Mathematics 61.1 (2013): 35-45. <http://eudml.org/doc/281314>.

@article{MrinalKantiRoychowdhury2013,
abstract = {We consider an inhomogeneous measure μ with the inhomogeneous part a self-similar measure ν, and show that for a given r ∈ (0,∞) the lower and the upper quantization dimensions of order r of μ are bounded below by the quantization dimension $D_r(ν)$ of ν and bounded above by a unique number $κ_r ∈ (0,∞)$, related to the temperature function of the thermodynamic formalism that arises in the multifractal analysis of μ.},
author = {Mrinal Kanti Roychowdhury},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {quantization dimension; inhomogeneous self-similar measure; temperature function},
language = {eng},
number = {1},
pages = {35-45},
title = {Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures},
url = {http://eudml.org/doc/281314},
volume = {61},
year = {2013},
}

TY - JOUR
AU - Mrinal Kanti Roychowdhury
TI - Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2013
VL - 61
IS - 1
SP - 35
EP - 45
AB - We consider an inhomogeneous measure μ with the inhomogeneous part a self-similar measure ν, and show that for a given r ∈ (0,∞) the lower and the upper quantization dimensions of order r of μ are bounded below by the quantization dimension $D_r(ν)$ of ν and bounded above by a unique number $κ_r ∈ (0,∞)$, related to the temperature function of the thermodynamic formalism that arises in the multifractal analysis of μ.
LA - eng
KW - quantization dimension; inhomogeneous self-similar measure; temperature function
UR - http://eudml.org/doc/281314
ER -