Szego's theorem for canonical systems: the Arov gauge and a sum rule

被引：3

作者：

Damanik, David ^{[1
]}

Eichinger, Benjamin ^{[1
]}

Yuditskii, Peter ^{[2
]}

机构：

[1] Rice Univ, Dept Math, 6100 Main MS 134, Houston, TX 77005 USA

[2] Johannes Kepler Univ Linz, Abt Dynam Syst & Approximationstheorie, Altenberger Str 69, A-4040 Linz, Austria

来源：

JOURNAL OF SPECTRAL THEORY | 2021年 / 11卷 / 03期

基金：

奥地利科学基金会;

关键词：

Szego class; canonical Hamiltonian system; sum rule; entropy; ENTROPY;

D O I：

10.4171/JST/371

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider canonical systems and investigate the Szego class, which is defined via the finiteness of the associated entropy functional. Noting that the canonical system may be studied in a variety of gauges, we choose to work in the Arov gauge, in which we prove that the entropy integral is equal to an integral involving the coefficients of the canonical system. This sum rule provides a spectral theory gem in the sense proposed by Barry Simon.

引用

页码：1255 / 1277

页数：23

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