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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Order problem for canonical systems and a conjecture of Valent

Author: R. Romanov
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 34L15, 47B36
Published electronically: May 3, 2016
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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.

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R. Romanov
Affiliation: Department of Mathematical Physics and Laboratory of Quantum Networks, Faculty of Physics, St. Petersburg State University, 198504, St. Petersburg, Russia

Keywords: Canonical systems, spectral asymptotics, Jacobi matrices, strings
Received by editor(s): September 22, 2014
Received by editor(s) in revised form: February 9, 2015
Published electronically: May 3, 2016
Additional Notes: This work was supported in part by the Austrian Science Fund (FWF) project I 1536–N25, the Russian Foundation for Basic Research, grants 13-01-91002-ANF and 12-01-00215, and by Project SPbSU
Article copyright: © Copyright 2016 American Mathematical Society