论文标题
Chebyshev多项式的渐近学，V。残留多项式
Asymptotics of Chebyshev Polynomials, V. Residual Polynomials
论文作者
论文摘要
我们研究残差多项式，$ r_ {x_0，n}^{（\ m athfrak {e}）} $，$ \ mathfrak {e} \ subset \ subset \ mathbb {r} $，$ x_0 \ in \ mathbb {r} $ r（x_0）= 1 $最小化$ \ sup $ norm上的$ \ mathfrak {e} $。在相当普遍的情况下，新的是其规范上的上限（在某些情况下是最佳的）和szegő-widom渐近学。我们还讨论了几个启发性的例子，并在复杂情况下进行了一些结果。
We study residual polynomials, $R_{x_0,n}^{(\mathfrak{e})}$, $\mathfrak{e}\subset\mathbb{R}$, $x_0\in\mathbb{R}\setminus\mathfrak{e}$, which are the degree at most $n$ polynomials with $R(x_0)=1$ that minimize the $\sup$ norm on $\mathfrak{e}$. New are upper bounds on their norms (that are optimal in some cases) and Szegő--Widom asymptotics under fairly general circumstances. We also discuss several illuminating examples and some results in the complex case.
