The inverse commutant lifting problem. II: Hellinger functional-model spaces (Q371831)

The earlier paper of the authors [Integral Equations Oper. Theory 70, No. 1, 17--62 (2011;Zbl 1244.47010)] was devoted to consideration of the Inverse Commutant Lifting Problem in terms of the geometry of operators and subspaces. The present paper uses Fourier representation operators to present a more concrete function-theoretic form of the previous results by making use of Hellinger functional-model spaces (Theorems 3.3, 4.3). The applications of the obtained results to the classical Nehari problem are considered, some connections with results of Adamjan-Arov-Krein on the inverse problem for the Nehari problem and with recent results on the more general Relaxed Commutant Lifting Problem are discussed.