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Mosc. Math. J., 2017, Volume 17, Number 1, Pages 35–49 (Mi mmj624)  

Spectral measure at zero for self-similar tilings

Jordan Emme

Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France

Abstract: The goal of this paper is to study the action of the group of translations over self-similar tilings in the Euclidean space $\mathbb R^d$. It investigates the behaviour near zero of spectral measures for such dynamical systems. Namely, the paper gives a Hölder asymptotic expansion near zero for these spectral measures. It is a generalization to higher dimension of a result by Bufetov and Solomyak who studied self similar-suspension flows for substitutions. The study of such asymptotics mostly involves the understanding of the deviations of some ergodic averages.

Key words and phrases: self-similar tilings, ergodic theory, spectral measures.

DOI: https://doi.org/10.17323/1609-4514-2017-17-1-35-49

Full text: http://www.mathjournals.org/.../2017-017-001-003.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 37B50, 37A30
Received: June 10, 2016; in revised form January 24, 2017
Language:

Citation: Jordan Emme, “Spectral measure at zero for self-similar tilings”, Mosc. Math. J., 17:1 (2017), 35–49

Citation in format AMSBIB
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\by Jordan~Emme
\paper Spectral measure at zero for self-similar tilings
\jour Mosc. Math.~J.
\yr 2017
\vol 17
\issue 1
\pages 35--49
\mathnet{http://mi.mathnet.ru/mmj624}
\crossref{https://doi.org/10.17323/1609-4514-2017-17-1-35-49}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3634519}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000402641900003}


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