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Lower bound for cyclic sums with one-sided maximal averages in denominatorsстатья
- Автор: Sadov Sergey
- Журнал: ArXiv e-prints
- Год издания: 2022
- Первая страница: 1
- Последняя страница: 21
- Номер статьи: arXiv:2210.00360 [math.CA]
- DOI: 10.48550/ARXIV.2210.00360
- Аннотация: Let x=(x_1,…,x_n) be an n-tuple of positive real numbers and the sequence (x_i)i∈ℤ be its n-periodic extension. Given an n-tuple r=(r_1,…,r_n) of positive integers, let a_i be the arithmetic mean of x_{i+1},…,x_{i+r_i}. We form the cyclic sums S_n(x,r)=∑x_i/a_i, following the pattern of the long studied Shapiro sums, which correspond to all r_i=2, and more general Diananda sums, where all r_i are equal. We find the asymptotics of the r-independent lower bounds A_{n,∗}=inf_r inf_x S_n(x,r) as n→∞: it is A_{n,∗}=e log n−A+O(1/log n).
- Добавил в систему: Садов Сергей Юрьевич