Geodesic
Inhomogeneous vector Riemann boundary value problem and convolutions equation on a finite interval
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2021), pp. 15-28

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

This paper proposes a method for investigating the inhomogeneous Riemann —Hilbert vector boundary value problem (also called the Riemann vector boundary value problem) in the Wiener algebra (to an convolution equation on a finite interval). The method consists in reducing the Riemann problem to a truncated Wiener —Hopf equation. It is shown that for the correct solvability of an inhomogeneous Riemann vector boundary value problem, it is necessary and sufficient to prove the uniqueness of the solution of the corresponding truncated homogeneous Wiener —Hopf equation. As a result of applying the method, new sufficient conditions for the existence of a canonical factorization of the function matrix in the Wiener algebra of order two are obtained.
Keywords: factorization, Riemann boundary value problem, matrix functions
Mots-clés : partial indices, convolutions equation. 
@article{IVM_2021_3_a1,
     author = {A. F. Voronin},
     title = {Inhomogeneous vector {Riemann} boundary value problem and convolutions equation on a finite interval},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {15--28},
     publisher = {mathdoc},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_3_a1/}
}
TY  - JOUR
AU  - A. F. Voronin
TI  - Inhomogeneous vector Riemann boundary value problem and convolutions equation on a finite interval
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2021
SP  - 15
EP  - 28
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2021_3_a1/
LA  - ru
ID  - IVM_2021_3_a1
ER  - 
%0 Journal Article
%A A. F. Voronin
%T Inhomogeneous vector Riemann boundary value problem and convolutions equation on a finite interval
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2021
%P 15-28
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2021_3_a1/
%G ru
%F IVM_2021_3_a1
A. F. Voronin. Inhomogeneous vector Riemann boundary value problem and convolutions equation on a finite interval. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2021), pp. 15-28. http://geodesic.mathdoc.fr/item/IVM_2021_3_a1/