Sum rules for Jacobi matrices and their applications to spectral theory

• 成果类型: Article
• 署名作者: Killip, R; Simon, B
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2003.158.253
• 发表日期: 2003
• 页码: 253-321
• 关键词: absolutely continuous-spectrum; dimensional schrodinger-operators; Orthogonal polynomials; decaying potentials; scattering-theory; toda lattice; bound-states; Finite; INTEGRALS; number

摘要

We discuss the proof of and systematic application of Case's sum rules for Jacobi matrices. Of special interest is a linear combination of two of his sum rules which has strictly positive terms. Among our results are a complete classification of the spectral measures of all Jacobi matrices J for which J - J(0) is Hilbert-Schmidt, and a proof of Nevai's conjecture that the Szego condition holds if J - J(0) is trace class.