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2 Bulletin of the Polish Academy of Sciences. Mathematics

2 Roychowdhury M. K.

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Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures

Roychowdhury M. K.

Bulletin of the Polish Academy of Sciences. Mathematics

2013

Vol. 61, no 1

35--45

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 Dr(ν) of ν and bounded above by a unique number κr∈(0,∞), related to the temperature function of the thermodynamic formalism that arises in the multifractal analysis of μ.

Quantization dimension function and ergodic measure with bounded distortion

Roychowdhury M. K.

Bulletin of the Polish Academy of Sciences. Mathematics

2009

Vol. 57, no 3-4

251-262

The quantization dimension function for the image measure of a shift-invariant ergodic measure with bounded distortion on a self-conformal set is determined, and its relationship to the temperature function of the thermodynamic formalism arising in multifractal analysis is established.