Order problem for canonical systems and a conjecture of Valent
- Resource Type
- Working Paper
- Authors
- Romanov, Roman
- Source
- Subject
- Mathematics - Spectral Theory
Mathematical Physics
34L15, 47B36
- Language
We establish a sharp upper estimate for the order of a canonical system in terms of the Hamiltonian. This upper estimate becomes an equality in the case of Krein strings. As an application we prove a conjecture of Valent about the order of a certain class of Jacobi matrices with polynomial coefficients.
Comment: 20 pages, submitted to Transactions AMS