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

David Damanik, Benjamin Eichinger, Peter Yuditskii

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish
Pages (from-to)1255-1277
Number of pages23
JournalJournal of Spectral Theory
Volume11
Issue number3
DOIs
StatePublished - 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021 European Mathematical Society.

Keywords

  • Canonical Hamiltonian system
  • Entropy
  • Sum rule
  • Szego class

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