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Seminar on Complex Analysis (Gonchar Seminar)
November 17, 2014 18:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)

Order problem for canonical systems and a conjecture of Valent.

R. V. Romanov

Saint Petersburg State University

Abstract: A precise upper estimate for the exponential order of the monodromy matrix of $2\times 2$ canonical systems is obtained. The estimate is shown to become an equality in the case of the Krein strings. As an application we prove a conjecture by Valent on the order for a certain class of indeterminate moment problems with polynomial Jacobi parameters related to birth–death processes.