Canonical Sequences of Optimal Quantization for Condensation Measures

Authors

Doğan Çömez
Mrinal Kanti Roychowdhury, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

5-28-2022

Abstract

We consider condensation measures of the form P:=13P∘S−11+13P∘S−12+13ν associated with the system (S,(13,13,13),ν), where S={Si}2i=1 are contractions and ν is a Borel probability measure on R with compact support. Let D(μ) denote the quantization dimension of a measure μ if it exists. In this paper, we study self-similar measures ν satisfying D(ν)>κ, D(ν)κ, the D(P)-dimensional lower and upper quantization coefficients are finite, positive and unequal; and for D(ν)≤κ, the D(P)-dimensional lower quantization coefficient is infinity.

We consider condensation measures of the form P:=13P∘S−11+13P∘S−12+13ν associated with the system (S,(13,13,13),ν), where S={Si}2i=1 are contractions and ν is a Borel probability measure on R with compact support. Let D(μ) denote the quantization dimension of a measure μ if it exists. In this paper, we study self-similar measures ν satisfying D(ν)>κ, D(ν)κ, the D(P)-dimensional lower and upper quantization coefficients are finite, positive and unequal; and for D(ν)≤κ, the D(P)-dimensional lower quantization coefficient is infinity.

Comments

© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG

https://rdcu.be/cTLFv https://arxiv.org/abs/1705.08811v4

Recommended Citation

Çömez, D., Roychowdhury, M.K. Canonical Sequences of Optimal Quantization for Condensation Measures. Qual. Theory Dyn. Syst. 21, 79 (2022). https://doi.org/10.1007/s12346-022-00610-0

Publication Title

Qualitative Theory of Dynamical Systems

DOI

10.1007/s12346-022-00610-0