Order problem for canonical systems and a conjecture of Valent

Romanov, R.

doi:10.1090/tran6686

Order problem for canonical systems and a conjecture of Valent
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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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