Perturbations of orthogonal polynomials with periodic recursion coefficients

被引：51

作者：

Damanik, David ^{[1
]}

Killip, Rowan ^{[2
]}

Simon, Barry ^{[3
]}

机构：

[1] Rice Univ, Dept Math, Houston, TX 77005 USA

[2] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[3] CALTECH, Pasadena, CA 91125 USA

来源：

ANNALS OF MATHEMATICS | 2010年 / 171卷 / 03期

关键词：

INVERSE SPECTRAL-ANALYSIS; C-ASTERISK-ALGEBRAS; MATRIX POLYNOMIALS; SUM-RULES; SCHRODINGER-OPERATORS; RELATIVE ASYMPTOTICS; JACOBI MATRICES; PARTIAL INFORMATION; RAKHMANOVS THEOREM; STURM-LIOUVILLE;

D O I：

10.4007/annals.2010.171.1931

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The results of Denisov-Rakhmanov, Szego-Shohat-Nevai, and Killip-Simon are extended from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC) to asymptotically periodic OPRL and OPUC. The key tool is a characterization of the isospectral torus that is well adapted to the study of perturbations.

引用

页码：1931 / 2010

页数：80

共 121 条

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AHEIZER NI, 1962, TRANSL MATH MONOGR, V2

[2] Some asymptotic properties for orthogonal polynomials with respect to varying measures [J].