Szeg\H{o}'s Theorem for Canonical Systems: the Arov Gauge and a Sum Rule

Autor:	Damanik, David, Eichinger, Benjamin, Yuditskii, Peter
Rok vydání:	2019
Předmět:	Mathematics - Spectral Theory Mathematical Physics Mathematics - Classical Analysis and ODEs
Druh dokumentu:	Working Paper
Popis:	We consider canonical systems and investigate the Szeg\H{o} 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. Comment: 17 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1907.03267 Zobrazit plný text záznamu View this record from Arxiv