Sum rules for Jacobi matrices and their applications to spectral theory
Sum rules for Jacobi matrices and their applications to spectral theory
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DOI：
10.4007/annals.2003.158.253
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发表时间：
2003-07-01
影响因子：
4.9
通讯作者：
Simon, B
中科院分区：
文献类型：
--
作者：
Killip, R;Simon, B
讨论了Jacobi矩阵的Case和规则的证明及其系统应用。特别有趣的是他的两个和规则的线性组合，它们有严格的正项。在我们的研究结果中，我们得到了J - J(0)为Hilbert-Schmidt的所有Jacobi矩阵J的谱测度的完全分类，并证明了Nevai关于当J - J(0)为迹类时Szego条件成立的猜想。
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.