| Autor: |
Yong-Shen Cao, Qi-Rong Deng, Ming-Tian Li |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Entropy, Vol 24, Iss 8, p 1142 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
1099-4300 |
| DOI: |
10.3390/e24081142 |
| Popis: |
This paper is devoted to the characterization of spectrum candidates with a new tree structure to be the spectra of a spectral self-similar measure μN,D generated by the finite integer digit set D and the compression ratio N−1. The tree structure is introduced with the language of symbolic space and widens the field of spectrum candidates. The spectrum candidate considered by Łaba and Wang is a set with a special tree structure. After showing a new criterion for the spectrum candidate with a tree structure to be a spectrum of μN,D, three sufficient and necessary conditions for the spectrum candidate with a tree structure to be a spectrum of μN,D were obtained. This result extends the conclusion of Łaba and Wang. As an application, an example of spectrum candidate Λ(N,B) with the tree structure associated with a self-similar measure is given. By our results, we obtain that Λ(N,B) is a spectrum of the self-similar measure. However, neither the method of Łaba and Wang nor that of Strichartz is applicable to the set Λ(N,B). |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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