Szegő’s theorem for canonical systems: the Arov gauge and a sum rule

IF 1 3区数学 Q1 MATHEMATICS

Journal of Spectral Theory Pub Date : 2019-07-07 DOI:10.4171/jst/371

D. Damanik, B. Eichinger, P. Yuditskii

引用次数: 3

Abstract

We consider canonical systems and investigate the Szegő 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.

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正则系统的塞格定理:Arov规范和求和规则

我们考虑正则系统并研究了通过相关熵泛函的有限性来定义的塞格格类。注意到正则系统可以在各种量规中研究，我们选择在Arov量规中工作，在Arov量规中，我们证明了熵积分等于涉及正则系统系数的积分。这个求和规则提供了Barry Simon提出的意义上的光谱理论宝石。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Spectral Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome. The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory. Schrödinger operators, scattering theory and resonances; eigenvalues: perturbation theory, asymptotics and inequalities; quantum graphs, graph Laplacians; pseudo-differential operators and semi-classical analysis; random matrix theory; the Anderson model and other random media; non-self-adjoint matrices and operators, including Toeplitz operators; spectral geometry, including manifolds and automorphic forms; linear and nonlinear differential operators, especially those arising in geometry and physics; orthogonal polynomials; inverse problems.