Absolute continuity of Bernoulli convolutions for algebraic parameters

IF 3.5 1区数学 Q1 MATHEMATICS

Journal of the American Mathematical Society Pub Date : 2016-01-31 DOI:10.1090/jams/916

P. P. Varj'u

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引用次数: 42

Abstract

We prove that Bernoulli convolutions μ λ \mu _\lambda are absolutely continuous provided the parameter λ \lambda is an algebraic number sufficiently close to 1 1 depending on the Mahler measure of λ \lambda .

查看原文本刊更多论文

代数参数的伯努利卷积的绝对连续性

我们证明了伯努利卷积μ λ \mu ＿ \lambda是绝对连续的，只要参数λ \lambda是一个足够接近于11的代数数，依赖于λ \lambda的马勒测度。

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来源期刊

Journal of the American Mathematical Society 数学-数学

CiteScore

7.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.