Order problem for canonical systems and a conjecture of Valent

2015/02/16 by Roman Romanov, Romanov, Roman
Mathematics · Physics and Astronomy · #34L15 #47B36 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:34L15 #msc:47B36

paper · pdf · doi:10.48550/arxiv.1502.04402

20 pages, submitted to Transactions AMS

arxiv created 2015/02/16 · arxiv updated 2015/02/17

Abstract

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.

Related

• Remling's Theorem on canonical systems
• The Canonical Symmetry and Hamiltonian Formalism. II. Hamiltonian Operators
• Estimates for the Weyl coefficient of a two-dimensional canonical system
• Growth estimates for Nevanlinna matrices of order larger than one half
• Combinatorics of linear stability for Hamiltonian systems in arbitrary dimension