Sobolev $p$ -范数下离零最小偏差多项式
Polynomials of least deviation from zero in Sobolev $p$-norm
摘要：
本文的第一部分补充了以前的结果的特征多项式的最小偏差从零索博列夫$p$ -范数（$1<p<\infty$）的情况下$p=1$。一些相关的例子表明。第二部分讨论了离散Sobolev $p$ -范数下最小偏差多项式的零点位置。在一般条件下建立了零点的渐近分布。在离散部分的某种阶限制下，证明了$n$阶最小偏差多项式在测度支撑的凸包上至少有$n-\mathbf{d}^*$零点，其中$\mathbf{d}^*$表示离散部分的项数.
英文摘要：
The first part of this paper complements previous results on characterization of polynomials of least deviation from zero in Sobolev $p$-norm ($1<p<\infty$) for the case $p=1$. Some relevant examples are indicated. The second part deals with the location of zeros of polynomials of least deviation in discrete Sobolev $p$-norm. The asymptotic distribution of zeros is established on general conditions. Under some order restriction in the discrete part, we prove that, the $n$-th polynomial of least deviation has at least $n-\mathbf{d}^*$ zeros on the convex hull of the support of the measure, where $\mathbf{d}^*$ denotes the number of terms in the discrete part.
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