Some extremal functions in fourier analysis. II
Some extremal functions in fourier analysis. II
复制标题
傅里叶分析中的一些极值函数。
DOI：
10.1090/s0002-9947-2010-04886-x
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发表时间：
2008
影响因子：
1.3
通讯作者：
J. Vaaler
中科院分区：
文献类型：
--
作者：
E. Carneiro;J. Vaaler
本文给出了一类包含对数的偶函数的指数型极值优子点|X|和|X| α，其中-1 < α < 1。我们也给出了这些结果的周期性版本，其中的优数和次数是有界次数的三角多项式。作为应用，我们得到了某些埃尔米特形式的最优估计，其中包括离散类似的一维Hardy-Littlewood-Sobolev不等式。进一步的应用提供了一个Erdos-Turan型不等式，该不等式根据多项式的根中的幂和来估计单位圆盘上的代数多项式的超范数。
We obtain extremal majorants and minorants of exponential type for a class of even functions on ℝ which includes log |x| and |x| α , where -1 < α < 1. We also give periodic versions of these results in which the majorants and minorants are trigonometric polynomials of bounded degree. As applications we obtain optimal estimates for certain Hermitian forms, which include discrete analogues of the one dimensional Hardy-Littlewood-Sobolev inequalities. A further application provides an Erdos- Turan-type inequality that estimates the sup norm of algebraic polynomials on the unit disc in terms of power sums in the roots of the polynomials.