Order problem for canonical systems and a conjecture of Valent
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🧮 math.SP
math-phmath.MP
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ordercanonicalconjectureestimateuppervalentapplicationbecomes
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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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