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

Damanik, David and Eichinger, Benjamin and Yuditskii, Peter (2021) Szego's theorem for canonical systems : The Arov gauge and a sum rule. Journal of Spectral Theory, 11 (3). pp. 1255-1277. ISSN 1664-039X

Abstract

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.