Asymptotic of the geometric mean error in the quantization of recurrent self-similar measures

Mrinal Kanti Roychowdhury; Nina Snigireva

doi:10.1016/j.jmaa.2015.05.063

Asymptotic of the geometric mean error in the quantization of recurrent self-similar measures

Mrinal Kanti Roychowdhury, Nina Snigireva

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

1 Citation (Scopus)

Abstract

Assuming a separation property, we determine the quantization dimension D(μ) of a recurrent self-similar measure μ with respect to the geometric mean error, and prove that D(μ) coincides with the Hausdorff dimension dimH*(μ) of μ.

Original language	English
Pages (from-to)	737-751
Number of pages	15
Journal	Journal of Mathematical Analysis and Applications
Volume	431
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2015.05.063
Publication status	Published - 15 Nov 2015
Externally published	Yes

Keywords

Geometric mean error
Hausdorff dimension
Quantization
Recurrent self-similar measure

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10.1016/j.jmaa.2015.05.063

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title = "Asymptotic of the geometric mean error in the quantization of recurrent self-similar measures",

abstract = "Assuming a separation property, we determine the quantization dimension D(μ) of a recurrent self-similar measure μ with respect to the geometric mean error, and prove that D(μ) coincides with the Hausdorff dimension dimH*(μ) of μ.",

keywords = "Geometric mean error, Hausdorff dimension, Quantization, Recurrent self-similar measure",

author = "Roychowdhury, \{Mrinal Kanti\} and Nina Snigireva",

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year = "2015",

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AU - Roychowdhury, Mrinal Kanti

AU - Snigireva, Nina

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N2 - Assuming a separation property, we determine the quantization dimension D(μ) of a recurrent self-similar measure μ with respect to the geometric mean error, and prove that D(μ) coincides with the Hausdorff dimension dimH*(μ) of μ.

AB - Assuming a separation property, we determine the quantization dimension D(μ) of a recurrent self-similar measure μ with respect to the geometric mean error, and prove that D(μ) coincides with the Hausdorff dimension dimH*(μ) of μ.

KW - Geometric mean error

KW - Hausdorff dimension

KW - Quantization

KW - Recurrent self-similar measure

UR - https://www.scopus.com/pages/publications/84937523191

U2 - 10.1016/j.jmaa.2015.05.063

DO - 10.1016/j.jmaa.2015.05.063

M3 - Article

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VL - 431

SP - 737

EP - 751

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Asymptotic of the geometric mean error in the quantization of recurrent self-similar measures

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Keywords

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