FACTORIZATION FORMULAS FOR SOME CLASSES OF GENERALIZED J-INNER MATRIX VALUED FUNCTIONS

摘要

The class U_K(j_(pq)) of generalized j_(pq)-inner matrix valued functions (mvf's) was introduced in [2], For a mvf W from a subclass U_k~r(j_(pq)) of U_K(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_k~?(j_(pq)) and for every mvf W ∈ U_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.