Generalised canonical systems related to matrix string equations: corresponding structured operators and high-energy asymptotics of the Weyl functions

We obtain high energy asymptotics of Titchmarsh-Weyl functions of the generalised canonical systems generalising in this way a seminal Gesztesy-Simon result. The matrix valued analog of the amplitude function satisfies in this case an interesting new identity. The corresponding structured operators are studied as well. MSC(2020): 34B20, 37J05, 47A48, 47A62

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