Construction of a factorization of a certain class of matrix functions in the Wiener algebra of order two
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2023), pp. 41-51.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper a representative class of matrix functions from the Wiener algebra of order 2 is found, which admits effective factorization. The factorization problem for elements of this class reduces to a truncated Wiener–Hopf equation with a contracting integral operator. The latter guarantees, as will be shown in the paper, the existence of canonical factorization and its construction for matrix functions from the class under consideration.
Keywords: factorization problem,partial indices, Wiener algebra, Riemann boundary value problem, truncated equation Wiener–Hopf.
@article{IVM_2023_3_a3,
     author = {A. F. Voronin},
     title = {Construction of a factorization of a certain class of matrix functions in the {Wiener} algebra of order two},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {41--51},
     publisher = {mathdoc},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_3_a3/}
}
TY  - JOUR
AU  - A. F. Voronin
TI  - Construction of a factorization of a certain class of matrix functions in the Wiener algebra of order two
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2023
SP  - 41
EP  - 51
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2023_3_a3/
LA  - ru
ID  - IVM_2023_3_a3
ER  - 
%0 Journal Article
%A A. F. Voronin
%T Construction of a factorization of a certain class of matrix functions in the Wiener algebra of order two
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2023
%P 41-51
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2023_3_a3/
%G ru
%F IVM_2023_3_a3
A. F. Voronin. Construction of a factorization of a certain class of matrix functions in the Wiener algebra of order two. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2023), pp. 41-51. http://geodesic.mathdoc.fr/item/IVM_2023_3_a3/

[1] Voronin A.F., “Some questions on the relationship of the factorization problem of matrix functions and the truncated Wiener-Hopf equation in the Wiener algebra”, Sib. Electron. Mat. Izv., 18:2 (2021), 1615–1624 | DOI | MR

[2] Voronin A.F., “Neodnorodnaya vektornaya kraevaya zadacha Rimana i uravnenie v svertkakh na konechnom intervale”, Izv. vuzov. Matem., 2021, no. 3, 15–28 | Zbl

[3] Voronin A.F., “O svyazi zadachi faktorizatsii v algebre Vinera i usechennogo uravneniya Vinera–Khopfa”, Izv. vuzov. Matem., 2020, no. 12, 22–31 | Zbl

[4] Voronin A.F., “K metodu faktorizatsii matrits-funktsii v algebre Vinera poryadka $2$”, Sib. zhurn. industrialn. matem., 25:2 (2022), 32–45

[5] Muskhelishvili N.I., Singulyarnye integralnye uravneniya, Nauka, M., 1968

[6] Voronin A.F., “Issledovanie zadachi $\mathbb R$-lineinogo sopryazheniya i usechennogo uravneniya Vinera–Khopfa”, Matem. tr., 22:2 (2019), 21–33 | MR | Zbl

[7] Zabreiko P.P., Koshelev A.I., Krasnoselskii M.A. i dr., Integralnye uravneniya, Nauka, M., 1968

[8] Gokhberg I.Ts., Krein M.G., “Sistemy integralnykh uravnenii na polupryamoi s yadrami, zavisyaschimi ot raznosti argumentov”, Usp. matem. nauk, 13:2 (80) (1958), 3–72 | Zbl