Abstract
We study the quantization for in-homogeneous self-similar measures µ supported on self-similar sets. Assuming the open set condition for the corresponding iterated function system, we prove the existence of the quantization dimension for µ of order r ∈ (0,∞) and determine its exact value ξ r . Furthermore, we show that, the ξ r -dimensional lower quantization coefficient for µ is always positive and the upper one can be infinite. A sufficient condition is given to ensure the finiteness of the upper quantization coefficient.
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Zhu, S. Asymptotics of the quantization errors for in-homogeneous self-similar measures supported on self-similar sets. Sci. China Math. 59, 337–350 (2016). https://doi.org/10.1007/s11425-015-5045-x
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DOI: https://doi.org/10.1007/s11425-015-5045-x
Keywords
- condensation system
- in-homogeneous self-similar measures
- quantization coefficient
- quantization dimension