Geodesic
Tree structure of spectra of spectral Moran measures with consecutive digits
Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 593-610

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DOI

Let $\{b_n\}_{n=1}^{\infty }$ be a sequence of integers larger than 1. We will study the harmonic analysis of the equal-weighted Moran measures $\mu _{\{b_n\},\{{\mathcal D}_n\}}$ with ${\mathcal D}_n=\{0,1,2,\ldots ,q_n-1\}$, where $q_n$ divides $b_n$ for all $n\geq 1.$ In this paper, we first characterize all the maximal orthogonal sets of $L^2(\mu _{\{b_n\},\{{\mathcal D}_n\}})$ via a tree mapping. By this characterization, we give some sufficient conditions for the maximal orthogonal set to be an orthonormal basis.
DOI : 10.4153/S0008439523000991
Mots-clés : Spectral measures, spectra, Moran measures, orthonormal basis 
Wang, Cong; Yin, Feng-Li. Tree structure of spectra of spectral Moran measures with consecutive digits. Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 593-610. doi: 10.4153/S0008439523000991
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     author = {Wang, Cong and Yin, Feng-Li},
     title = {Tree structure of spectra of spectral {Moran} measures with consecutive digits},
     journal = {Canadian mathematical bulletin},
     pages = {593--610},
     year = {2024},
     volume = {67},
     number = {3},
     doi = {10.4153/S0008439523000991},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000991/}
}
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