\(J\)-inner matrix functions, interpolation and inverse problems for canonical systems. IV: Direct and inverse bitangential input scattering problems (Q1600091)

The paper is a continuation of the authors' investigations [Part I, Integral Equations Oper. Theory 29, No. 4, 373--454 (1997; Zbl 0902.30026]), II, ibid. 36, No. 1, 11--70 (2000; Zbl 0951.30029), III, ibid. 36, No. 2, 127--181 (2000; Zbl 0998.30037)] of inverse problems for canonical differential and integral systems of equations. In the paper under review the inverse input scattering problems are formulated and analyzed for canonical integral systems. Special attention is paid to the case when the input scattering matrix is of Wiener class. Formulas for the solution of the inverse input scattering problem are obtained by reproducing kernel Hilbert space methods. A number of illustrative examples are presented. For Part v, cf. ibid. 43, No.1, 68-129 (2002; Zbl 1009.34007).