Tohoku Mathematical Journal
2022
December
SECOND SERIES VOL. 74, NO. 4

Tohoku Math. J.
74 (2022), 549-568

Title AN INVERSE PROBLEM FOR A CLASS OF LACUNARY CANONICAL SYSTEMS WITH DIAGONAL HAMILTONIAN

Author Masatoshi Suzuki

(Received June 18, 2021, revised August 10, 2021)
Abstract. Hamiltonians are 2-by-2 positive semidefinite real symmetric matrix-valued functions satisfying certain conditions. In this paper, we solve the inverse problem for which recovers a Hamiltonian from the solution of a first-order system attached to a given Hamiltonian, consisting of ordinary differential equations parametrized by a set of complex numbers, under certain conditions for the solutions. This inverse problem is a generalization of the inverse problem for two-dimensional canonical systems.

Mathematics Subject Classification. Primary 34A55; Secondary 31A10, 34L40.
Key words and phrases. Canonical systems, inverse problem.

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