Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures

Volume 61 / 2013

Mrinal Kanti Roychowdhury Bulletin Polish Acad. Sci. Math. 61 (2013), 35-45 MSC: Primary 28A80; Secondary 60D05, 94A15. DOI: 10.4064/ba61-1-5

Abstract

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 $.

Authors

  • Mrinal Kanti RoychowdhuryDepartment of Mathematics
    The University of Texas – Pan American
    1201 West University Drive
    Edinburg, TX 78539-2999, U.S.A.
    e-mail

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