BERNOULLI CONVOLUTIONS ASSOCIATED WITH CERTAIN NON——PISOT NUMBERS |
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作者姓名: | FengDejun WangYang |
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作者单位: | [1]TsinghuaUniversity,China [2]GeorgiaInstituteofTechnology,USA |
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摘 要: | The Bernoulli convolution Vλ measure is shown to be absolutely continuous with L^2 density for almost all 1/2<λ<1, and singular if λ^-1 is a Pisot number. It is an open question whether the Pisot type Bernoulli conuolutions are the only singular ones. In this paper, we construct a family of non-Pisot type Bernoulli convo-lutions Vλ such that their density functions, if they exist, are not L^2. We also construct other Bernolulli convo-lutions whose density functions if they exist, behave rather badly.
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关 键 词: | Bernoulli卷积 自我相似测量法 Pisot数 Salem数 密度函数 随机序列 级数 |
收稿时间: | 26 July 2003 |
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