Factorization formulas for some classes of generalized \(J\)-inner matrix valued functions. (English) Zbl 1324.47032

The class \(U_\kappa (j_{pq})\), \(j_{pq}=\operatorname{diag}(I_p, -I_q)\), of generalized \(j_{pq}\)-inner matrix valued functions (mvf’s) corresponding to kernels with \(\kappa\) negative squares was introduced by D. Alpay and H. Dym [Oper. Theory, Adv. Appl. 18, 89–159 (1986; Zbl 0594.46022)] in connection with some indefinite interpolation problems. V. Derkach and H. Dym [Integral Equations Oper. Theory 65, No. 1, 1–50 (2009; Zbl 1185.47015)] proved factorization formulas for mvf’s from a subclass \(U^r_\kappa (j_{pq})\).
In the paper under review, the author introduces a dual class \(U^l_\kappa (j_{pq})\), proves appropriate factorization formulas, and introduces and studies singular generalized \(j_{pq}\)-inner mvf’s.


47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
30J05 Inner functions of one complex variable