Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 2, pp. 382-386
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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/
@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},
year = {1964},
volume = {9},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a19/}
}
TY - JOUR
AU - Yu. L. Šmul'yan
TI - Optimum Factorization of the Non-negative Matrix Functions
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1964
SP - 382
EP - 386
VL - 9
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a19/
LA - ru
ID - TVP_1964_9_2_a19
ER -
%0 Journal Article
%A Yu. L. Šmul'yan
%T Optimum Factorization of the Non-negative Matrix Functions
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1964
%P 382-386
%V 9
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a19/
%G ru
%F TVP_1964_9_2_a19
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 $$ A(e^{-i\lambda})A^*(e^{-i\lambda})=2\pi f(\lambda). $$
