Bounds on Orthonormal Polynomials for Restricted Measures

被引：0

作者：

Lubinsky, D. S. ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

CONSTRUCTIVE APPROXIMATION | 2025年 / 61卷 / 03期

关键词：

Orthogonal polynomials; Bounds; Restricted measures; ORTHOGONAL POLYNOMIALS; GROWTH; ZEROS;

D O I：

10.1007/s00365-023-09671-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose that. is a given positive measure on [-1, 1], and that mu is another measure on the real line, whose restriction to (-1, 1) is nu. We show that one can bound the orthonormal polynomials p(n) (mu, y) for mu and y is an element of R, by the supremum of | S-J ( y) p(n-J) (S-j(2)nu, y )|, where the sup is taken over all 0 <= J <= n and all monic polynomials S-J of degree J with zeros in an appropriate set.

引用

页码：615 / 645

页数：31

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