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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Order problem for canonical systems and a conjecture of Valent
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by R. Romanov PDF
Trans. Amer. Math. Soc. 369 (2017), 1061-1078 Request permission

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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Additional Information
  • R. Romanov
  • Affiliation: Department of Mathematical Physics and Laboratory of Quantum Networks, Faculty of Physics, St. Petersburg State University, 198504, St. Petersburg, Russia
  • Email: morovom@gmail.com
  • 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 11.38.263.2014
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 1061-1078
  • MSC (2010): Primary 34L15, 47B36
  • DOI: https://doi.org/10.1090/tran6686
  • MathSciNet review: 3572264