Geodesic
A Factorization Problem on a Smooth Two-Dimensional Surface
Matematičeskie zametki, Tome 108 (2020) no. 2, pp. 285-290

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Given a continuous complex-valued function $a$ and nonnegative functions $\rho_1$ and $\rho_2$ on a two-dimensional smooth connected closed surface such that $|a|=\rho_1\rho_2$ and the functions $\rho_1$ and $\rho_2$ have no common zeros, it is required to find complex-valued continuous functions $a_1$ and $a_2$ satisfying the conditions $a_1a_2=a$ and $|a_j|=\rho_j$. Necessary and sufficient solvability conditions for this problem are given.
Keywords: closed surface, factorization problem
Mots-clés : Cauchy index. 
@article{MZM_2020_108_2_a10,
     author = {A. P. Soldatov},
     title = {A {Factorization} {Problem} on a {Smooth} {Two-Dimensional} {Surface}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {285--290},
     publisher = {mathdoc},
     volume = {108},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_2_a10/}
}
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A. P. Soldatov. A Factorization Problem on a Smooth Two-Dimensional Surface. Matematičeskie zametki, Tome 108 (2020) no. 2, pp. 285-290. http://geodesic.mathdoc.fr/item/MZM_2020_108_2_a10/