The absolutely continuous spectrum of Jacobi matrices

• 成果类型: Article
• 署名作者: Remling, Christian
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.174.1.4
• 发表日期: 2011
• 页码: 125-171
• 关键词: singular continuous-spectrum; dimensional schrodinger-operators; sparse potentials; perturbations; asymptotics; POLYNOMIALS

摘要

I explore some consequences of a groundbreaking result of Breimesser and Pearson on the absolutely continuous spectrum of one-dimensional Schrodinger operators. These include an Oracle Theorem that predicts the potential and rather general results on the approach to certain limit potentials. In particular, we prove a Denisov-Rakhmanov type theorem for the general finite gap case. The main theme is the following: It is extremely difficult to produce absolutely continuous spectrum in one space dimension and thus its existence has strong implications.