Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures

• Autorzy: Mrinal Kanti Roychowdhury
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2013
• Tom: 61
• Numer: 1
• Strony: 35-45

Daty

wydano

2013

Twórcy

autor

Mrinal Kanti Roychowdhury

• Department of Mathematics, The University of Texas - Pan American, 1201 West University Drive, Edinburg, TX 78539-2999, U.S.A.

Identyfikatory

DOI

10.4064/ba61-1-5