论文标题
重点不平等
Pointwise Remez inequality
论文作者
论文摘要
标准著名的雷姆不平等现象对$ [-1,1] $的多项式值的值进行了更高的估计，如果它们在$ [ - 1,1] $的固定Lebesgue量度的子集上以$ 1 $的限制。极端溶液由重新验证的Chebyshev多项式进行一个间隔。 Andrievskii询问了多项式在固定点上的最大值，以便在一组固定尺寸上再次限制$ 1 $。我们表明，极端多项式是Chebyshev（一个间隔）或Akhiezer多项式（两个间隔），并证明了Totik-Widom的极值界限，从而为Andreievskii问题提供了完整的渐近解决方案。
The standard well-known Remez inequality gives an upper estimate of the values of polynomials on $[-1,1]$ if they are bounded by $1$ on a subset of $[-1,1]$ of fixed Lebesgue measure. The extremal solution is given by the rescaled Chebyshev polynomials for one interval. Andrievskii asked about the maximal value of polynomials at a fixed point, if they are again bounded $1$ on a set of fixed size. We show that the extremal polynomials are either Chebyshev (one interval) or Akhiezer polynomials (two intervals) and prove Totik-Widom bounds for the extremal value, thereby providing a complete asymptotic solution to the Andrievskii problem.
