Geodesic
Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures
Mrinal Kanti Roychowdhury1
1 Department of Mathematics The University of Texas – Pan American 1201 West University Drive Edinburg, TX 78539-2999, U.S.A.
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 1, pp. 35-45

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider an inhomogeneous measure $\mu $ with the inhomogeneous part a self-similar measure $\nu $, and show that for a given $r\in (0,\infty )$ the lower and the upper quantization dimensions of order $r$ of $\mu $ are bounded below by the quantization dimension $D_r(\nu )$ of $\nu $ and bounded above by a unique number $\kappa _r\in (0, \infty )$, related to the temperature function of the thermodynamic formalism that arises in the multifractal analysis of $\mu $.
DOI : 10.4064/ba61-1-5
Keywords: consider inhomogeneous measure inhomogeneous part self similar measure given infty lower upper quantization dimensions order bounded below quantization dimension bounded above unique number kappa infty related temperature function thermodynamic formalism arises multifractal analysis

Mrinal Kanti Roychowdhury 1

1 Department of Mathematics The University of Texas – Pan American 1201 West University Drive Edinburg, TX 78539-2999, U.S.A. 
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Mrinal Kanti Roychowdhury. Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 1, pp. 35-45. doi: 10.4064/ba61-1-5

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