A Maximal Function Approach to Christoffel Functions and Nevai’s Operators

被引：0
作者：
D. S. Lubinsky
机构：
[1] Georgia Institute of Technology,School of Mathematics
来源：
Constructive Approximation | 2011年 / 34卷
关键词：
Orthogonal polynomials on the real line; Christoffel functions; Ratio asymptotics; Nevai’s operators; 42C05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let μ be a compactly supported positive measure on the real line, with associated Christoffel functions λn(dμ,⋅). Let g be a measurable function that is bounded above and below on supp[μ] by positive constants. We show that λn(g  dμ,⋅)/λn(dμ,⋅)→g in measure in {x:μ′(x)>0} and consequently in all Lp norms, p<∞. The novelty is that there are no local or global restrictions on μ. The main idea is a new maximal function estimate for the “tail” in Nevai’s operators.
引用
收藏
页码：357 / 369
页数：12
相关论文
共 15 条
  • [1] Della Vecchia B.(2002)Uniform approximation by Nevai operators J. Approx. Theory 116 28-48
  • [2] Lasser R.(2003)Selective approximate identities for orthogonal polynomial sequences J. Math. Anal. Appl. 279 339-349
  • [3] Obermaier J.(1990)Relative asymptotics for polynomials orthogonal on the real axis Math. USSR. Sb. 65 505-529
  • [4] Lopez G.(1987)Extensions of Szegő’s theory of orthogonal polynomials, II Constr. Approx. 3 51-72
  • [5] Maté A.(1987)Extensions of Szegő’s theory of orthogonal polynomials, III Constr. Approx. 3 73-96
  • [6] Nevai P.(1991)Szegő’s extremum problem on the unit circle Ann. Math. 134 433-453
  • [7] Totik V.(1986)Orthogonal polynomials and Christoffel functions: a case study J. Approx. Theory 48 3-167
  • [8] Maté A.(undefined)undefined undefined undefined undefined-undefined
  • [9] Nevai P.(undefined)undefined undefined undefined undefined-undefined
  • [10] Totik V.(undefined)undefined undefined undefined undefined-undefined
12