Geodesic
Approximate factorization for one class of second-order matrix functions
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 4, pp. 511-529

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Approximate factorization of Holder matrix function on a simple smooth closed contour has been defined. Components for one class of the $2\times2$ matrix function have been approximated by polynomials in $z$ and $1/z$. Sufficient conditions have been found for zero equality of the partial indices of the approximating matrix function. Factorization of the approximating matrix function has been constructed in an explicit form.
Keywords: matrix function, factorization, approximate factorization. 
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     author = {S. N. Kiyasov},
     title = {Approximate factorization for one class of second-order matrix functions},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {511--529},
     publisher = {mathdoc},
     volume = {158},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2016_158_4_a4/}
}
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S. N. Kiyasov. Approximate factorization for one class of second-order matrix functions. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 4, pp. 511-529. http://geodesic.mathdoc.fr/item/UZKU_2016_158_4_a4/