Operator model and a trace formula for pairs of unitary operators

Daniel Alpay; Fabrizio Colombo; Izchak Lewkowicz; Irene Sabadini

Operator model and a trace formula for pairs of unitary operators

Functional Analysis 2026-07-06 v1

Authors: Daniel Alpay , Fabrizio Colombo , Izchak Lewkowicz , Irene Sabadini

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.

Keywords

trace formula unitary operators reproducing kernel Hilbert spaces Carathéodory function discrete systems

Cite

@article{arxiv.2607.05334,
  title  = {Operator model and a trace formula for pairs of unitary operators},
  author = {Daniel Alpay and Fabrizio Colombo and Izchak Lewkowicz and Irene Sabadini},
  journal= {arXiv preprint arXiv:2607.05334},
  year   = {2026}
}