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arXiv · 2607.05334

Operator model and a trace formula for pairs of unitary operators

Daniel Alpay·Fabrizio Colombo·Izchak Lewkowicz·Irene Sabadini
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Abstract

Using the theory of reproducing kernel Hilbert spaces introduced by L. de Branges and J. Rovnyak we prove a trace formula for pairs of operators in Hilbert space in terms of a Carath\'eodory function. We consider the special case, when the latter is rational. An application to the theory of first order discrete systems is given.

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Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini. 2026-07-06. Operator model and a trace formula for pairs of unitary operators. https://arxiv.org/abs/2607.05334

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