Factorization formulas for some classes of generalized J-inner matrix valued functions - Sukhorukova, O. (Methods of Functional Analysis and Topology, 2014)
The class U_κ(j_pq) of generalized j_pq-inner matrix valued functions (mvf’s) %and its subclass U^r_κ(j_pq) was introduced in [2]. For a mvf W from a subclass U^r_κ(j_pq) of U_κ(j_pq) the notion of the right associated pair was introduced in [13] and some factorization formulas were found. In the present paper we introduce a dual subclass U^_κ(j_pq) and for every mvf WU^_κ(j_pq) a left associated pair {β_1,β_2} is defined and factorization formulas for W in terms of β_1,β_2 are found. The notion of a singular generalized j_pq-inner mvf W is introduced and a characterization of singularity of W is given in terms of associated pair.