Perturbations of orthogonal polynomials with periodic recursion coefficients

• 成果类型: Article
• 署名作者: Damanik, David; Killip, Rowan; Simon, Barry
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.171.1931
• 发表日期: 2010
• 页码: 1931-2010
• 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

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.