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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 of ν and bounded above by a unique number , related to the temperature function of the thermodynamic formalism that arises in the multifractal analysis of μ.
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 -