On a family of singular continuous measures related to the doubling map

被引：1

作者：

Baake, Michael ^{[1
]}

Coons, Michael ^{[2
]}

Evans, James ^{[2
]}

Gohlke, Philipp ^{[1
]}

机构：

[1] Univ Bielefeld, Fak Math, Postfach 100131, D-33501 Bielefeld, Germany

[2] Univ Newcastle, Sch Math & Phys Sci, Univ Dr, Callaghan, NSW 2308, Australia

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2021年 / 32卷 / 04期

关键词：

Riesz products; Doubling map; Fourier analysis; Singular continuous measures; g-measures; Recurrences; Hyperuniformity; Scaling laws; MULTIFRACTAL ANALYSIS; INVARIANT-MEASURES; SCALING PROPERTIES; UNIQUENESS; OPERATOR;

D O I：

10.1016/j.indag.2021.06.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Here, we study some measures that can be represented by infinite Riesz products of 1-periodic functions and are related to the doubling map. We show that these measures are purely singular continuous with respect to Lebesgue measure and that their distribution functions satisfy super-polynomial asymptotics near the origin, thus providing a family of extremal examples of singular measures, including the Thue-Morse measure. (C) 2021 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

引用

页码：847 / 860

页数：14

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