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 language | English |
|---|---|
| Pages (from-to) | 1255-1277 |
| Number of pages | 23 |
| Journal | Journal of Spectral Theory |
| Volume | 11 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2021 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2021 European Mathematical Society.
Funding
1 David Damanik was supported in part by NSF grant DMS–1700131 and by an Alexander von Humboldt Foundation research award. 2 Benjamin Eichinger was supported by the Austrian Science Fund FWF, project no: J 4138-N32. 3 Peter Yuditskii was supported by the Austrian Science Fund FWF, project no: P29363-N32. Acknowledgements. P. Yuditskii would like to thank David Müller for helpful discussions. D. Damanik and B. Eichinger were supported in part by Austrian Science Fund FWF, project no. P29363-N32.
| Funders | Funder number |
|---|---|
| National Science Foundation | DMS–1700131 |
| Alexander von Humboldt-Stiftung | |
| Austrian Science Fund | J 4138-N32, P29363-N32 |
Keywords
- Canonical Hamiltonian system
- Entropy
- Sum rule
- Szego class