The law of the iterated logarithm for lacunary trigonometric series.
The law of the iterated logarithm for lacunary trigonometric series.
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缺位三角级数的迭代对数定律。
DOI：
10.1090/s0002-9947-1959-0108681-8
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发表时间：
1959
影响因子：
1.3
通讯作者：
M. Weiss
中科院分区：
文献类型：
--
作者：
M. Weiss
在这个定理中，ak和bk是实数，nk是正的，但不一定是积分。后一点对于应用程序很重要。缺项级数的重对数律在文献中已有论述。首先，Salem和Zygmund[i](方括号中的数字指的是论文末尾的参考书目)表明，在假设(1.2)下，我们有(1.3)与“？”它们还假定nk是整数。然而，后来鄂尔多斯和Gal[i]在限制下给出了(1.3)的完整证明
In this theorem the ak and bk are real and the nk are positive but not necessarily integral. The latter point is important for applications. The Law of the Iterated Logarithm for lacunary series has already been treated in the literature. In the first place, Salem and Zygmund [I ] (numbers in square brackets refer to the bibliography at the end of the paper) have shown that under the hypotheses (1.2) we have (1.3) with " ?" instead of ." They also presuppose that the nk are integers. A complete proof of (1.3) was given later by Erdos and Gal [I] under the restriction however