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| 关于Bernoulli卷积的一个谱性质 | |
| 引用本文： | 刘春苔,李泽芳. 关于Bernoulli卷积的一个谱性质[J]. 武汉工业学院学报, 2010, 29(1): 103-104,108. DOI: 10.3969/j.issn.1009-4881.2010.01.028 |
| 作者姓名： | 刘春苔 李泽芳 |
| 作者单位： | 1. 武汉工业学院,数理科学系,湖北,武汉,430023 2. 武汉职业技术学院,计算机系,湖北,武汉,430047 |
| 摘 要： | 设μρ是R上的参数为0〈ρ〈1的Bernoulli卷积测度，Hu和Lau证明了L2（μ）空间中含有一个无限指数型正交序列的充要条件是ρ是分数P／q的方根，其中P为奇数，q为偶数．本文讨论当ρ为其余情形时，指数型正交序列集中元素个数，证明了当ρ-不是奇数型方程的根或者其本原最小多项式g（x）满足g（l）为奇数时，则L2（μ）中任何指数型正交集至多含有两个元素． |
| 关 键 词： | Bernoulli卷积测度 最小本原多项式 正交集 |
A spectral property of the Bernoulli convolutions |
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| LIU Chun-tai,LI Ze-fang. A spectral property of the Bernoulli convolutions[J]. Journal of Wuhan Polytechnic University, 2010, 29(1): 103-104,108. DOI: 10.3969/j.issn.1009-4881.2010.01.028 | |
| Authors: | LIU Chun-tai LI Ze-fang |
| Affiliation: | LIU Chun-tai1,LI Ze-fang2(1.Department of Mathematics , Physics,Wuhan Polytechnic University,Wuhan 430023,China,2.Department of Computer,Wuhan Institute of Technology,Wuhan 430047,China) |
| Abstract: | Let be the Bernoulli convolution associated with on.Hu and Lau proved that the space contained an infinite orthonormal set of exponential functions if and only if is the nth root of a fraction where is odd and even.In this paper,we discuss the number of the orthonormal set of exponential function in other cases.And we prove that either isn't a root of a equation of odd type or is even,any orthonormal set of exponential function in has at most two elements,where is the minimal primitives polynomial for. |
| Keywords: | Bernoulli convolution minimal primitives polynomial orthonormal set |
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