在测度上离零最小的三角多项式及有关问题
Trigonometric polynomials deviating the least from zero in measure and related problems
摘要：
我们给出了三角多项式$f_n$与给定的领先谐波$y\cos nt$的问题的解决方案，偏离最少从零的措施，更准确地说，相对于功能$μ(f_n)=mes\{t\in[0,2π]: |f_n(t)|\ge 1\}$。对于三角多项式与一个固定的领先谐波，我们认为最小的一致偏差从零上的紧集，并找到极小值的偏差紧子集的环面，有一个给定的措施。本文给出了单位圆上零点在圆上的代数多项式的一个类似问题的一种解法。
英文摘要：
We give a solution of the problem on trigonometric polynomials $f_n$ with the given leading harmonic $y\cos nt$ that deviate the least from zero in measure, more precisely, with respect to the functional $μ(f_n)=mes\{t\in[0,2π]: |f_n(t)|\ge 1\}$. For trigonometric polynomials with a fixed leading harmonic, we consider the least uniform deviation from zero on a compact set and find the minimal value of the deviation over compact subsets of the torus that have a given measure. We give a solution of a similar problem on the unit circle for algebraic polynomials with zeros on the circle.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
