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.

中文翻译：

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典型系统的 Szegő 定理：Arov 规范和求和规则

我们考虑规范系统并研究 Szegő 类，它是通过相关熵函数的有限性定义的。注意到可以在各种规范中研究规范系统，我们选择在 Arov 规范中工作，我们证明熵积分等于涉及规范系统系数的积分。这个总和规则提供了巴里西蒙提出的意义上的光谱理论宝石。