Schur Functions and Inner Functions on the Bidisc

We study representations of inner functions on the bidisc from a fractional linear transformation point view. provide sufficient conditions, in terms colligation matrices, for existence two-variable functions. Here conditions are not necessary general, and we prove weak converse rational that admit one variable factorization. present classification de Branges–Rovnyak kernels (which also works setting polydisc open unit ball \({\mathbb {C}}^n\), \(n \ge 1\)). classify, Agler kernels, Schur