Semantic Scholar Open Access 2019 673 sitasi

Quantization

Yun Q. Shi Huifang Sun

Abstrak

. Let { f i } Ni =1 be a set of equi-contractive similitudes on R 1 satisfying the ﬁnite-type condition. We study the asymptotic quantization error for the self-similar measures µ associated with { f i } Ni =1 and a positive probability vector. With a veriﬁable assumption, we prove that the upper and lower quantization coeﬃcient for µ are both bounded away from zero and inﬁnity. This can be regarded as an extension of Graf and Luschgy’s result on self-similar measures with the open set condition. Our result is applicable to a signiﬁcant class of self-similar measures with overlaps, including Erd¨os measure, the 3-fold convolution of the classical Cantor measure and the self-similar measures on some λ -Cantor sets.

Penulis (2)

Yun Q. Shi

Huifang Sun

Format Sitasi

APA MLA BibTeX

Shi, Y.Q., Sun, H. (2019). Quantization. https://doi.org/10.1201/9781420007268-2

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Informasi Jurnal

Tahun Terbit: 2019
Bahasa: en
Total Sitasi: 673×
Sumber Database: Semantic Scholar
DOI: 10.1201/9781420007268-2
Akses: Open Access ✓