Geodesic
A Factorization Method for Products of Holomorphic Matrix Functions
Matematičeskie zametki, Tome 100 (2016) no. 2, pp. 212-228

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A class of matrix functions defined on a contour which bounds a finitely connected domain in the complex plane is considered. It is assumed that each matrix function in this class can be explicitly represented as a product of two matrix functions holomorphic in the outer and the inner part of the contour, respectively. The problem of factoring matrix functions in the class under consideration is studied. A constructive method reducing the factorization problem to finitely many explicitly written systems of linear algebraic equations is proposed. In particular, explicit formulas for partial indices are obtained.
Keywords: matrix function, factorization, partial index. 
@article{MZM_2016_100_2_a2,
     author = {A. G. Kamalian},
     title = {A {Factorization} {Method} for {Products} of {Holomorphic} {Matrix} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {212--228},
     publisher = {mathdoc},
     volume = {100},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_2_a2/}
}
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A. G. Kamalian. A Factorization Method for Products of Holomorphic Matrix Functions. Matematičeskie zametki, Tome 100 (2016) no. 2, pp. 212-228. http://geodesic.mathdoc.fr/item/MZM_2016_100_2_a2/