Spectra of Self-Similar Measures.
Entropy (Basel)
; 24(8)2022 Aug 17.
Article
em En
| MEDLINE
| ID: mdl-36010806
ABSTRACT
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 Laba 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 Laba 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 Laba and Wang nor that of Strichartz is applicable to the set Λ(N,B).
Texto completo:
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Base de dados:
MEDLINE
Idioma:
En
Revista:
Entropy (Basel)
Ano de publicação:
2022
Tipo de documento:
Article
País de afiliação:
China