A canonical factorization for meromorphic Herglotz functions on the unit disk and sum rules for Jacobi matrices

被引：19

作者：

Simon, B ^{[1
]}

机构：

[1] CALTECH, Div Phys Math & Astron, Pasadena, CA 91125 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2004年 / 214卷 / 02期

基金：

美国国家科学基金会;

关键词：

Herglotz; sum rules; Jacobi matrices;

D O I：

10.1016/j.jfa.2003.11.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a general canonical factorization for meromorphic Herglotz functions on the unit disk whose notable elements are that there is no restriction (other than interlacing) on the zeros and poles for their Blaschke product to converge and there is no singular inner function. We use this result to provide a significant simplification in the proof of Killip-Simon (Ann. Math. 158 (2003) 253) of their result characterizing the spectral measures of Jacobi matrices, J, with J - J(0) Hilbert-Schmidt. We prove a nonlocal version of Case and step-by-step sum rules. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：396 / 409

页数：14

共 38 条

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