Geodesic
Optimum Factorization of the Non-negative Matrix Functions
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 2, pp. 382-386

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The proposition about optimum factorization of a non-negative matrix function $f(\lambda)$ is generalized for the case where the unknown function $A(z)$ of class $H_2$ satisfies the inequality $$ A(e^{-i\lambda})A^*(e^{-i\lambda})\leqq 2\pi f(\lambda) $$ instead of the usual equality $$ A(e^{-i\lambda})A^*(e^{-i\lambda})=2\pi f(\lambda). $$ 
@article{TVP_1964_9_2_a19,
     author = {Yu. L. \v{S}mul'yan},
     title = {Optimum {Factorization} of the {Non-negative} {Matrix} {Functions}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {382--386},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {1964},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a19/}
}
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Yu. L. Šmul'yan. Optimum Factorization of the Non-negative Matrix Functions. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 2, pp. 382-386. http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a19/