Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szego asymptotics

• 成果类型: Article
• 署名作者: Damanik, David; Simon, Barry
• 署名单位: California Institute of Technology
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-005-0485-5
• 发表日期: 2006
• 页码: 1-50
• 关键词: dimensional schrodinger-operators; SUM-RULES; Orthogonal polynomials; spectral properties; wave-operators; integration; SCATTERING

摘要

We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szego asymptotics off the real axis. A key idea is to prove the equivalence of Szego asymptotics and of Jost asymptotics for the Weyl solution. We also prove L-2 convergence of Szego asymptotics on the spectrum.