Description of scattering matrices of unitary extensions of isometric operators in Pontryagin space (Q2440006)

The classical formula that represents all scattering matrices as a linear fractional transform of a Schur function is derived in a general setting of Pontryagin spaces. This formula is used for very general forms of classical interpolation problems of Nevanlinna-Pick type. This relates to the explicit formula for the \(\mathfrak{L}\)-resolvent of an isometric operator on such spaces. Therefore, boundary operator techniques are used as introduced in [\textit{T. Ya. Azizov} and \textit{I. S. Iokhvidov}, Foundations of the theory of linear operators in spaces with indefinite metric. (Osnovy teorii linejnykh operatorov v prostranstvakh s indefinitnoj metrikoj). Moskva: ''Nauka''. Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury (1986; Zbl 0607.47031)].