On several aspects of \(J\)-inner functions in Schur analysis (Q1281115)

The paper is a survey devoted to present different subjets of Schur analysis. The authors play a particular attention to their so called \(J\)-inner functions and they concentrate on the Soviet roots of the theory. We can find several sections: Classical interpolation problems, Blaschke products and the Nevanlinna-Pick algorithm; Darlington synthesis and scattering theory; Operator theoretic interpolation problems and dilation theory; Potapov factorization of \(J\)-contractive functions; Non-negative definite kernels, fundamental matrix inequality, fundamental indentities and the generalized Nehari problem; Arov's investigations on Darlington realization generated by \(J\)-inner functions; On \(J\)-inner functions and generalized bitangential Schur-Nevanlinna-Pinck interpolation. The paper contains 166 references.