Abstract:
In this paper, the homogeneous vector Riemann boundary value problem (factorization problem) is investigated from a new position — the Riemann problem is reduced to the truncated Wiener–Hopf equation (convolution equation on finite interval). In this paper, we find a connection between the problem of factorization of the matrix-function in the Wiener algebra of order two and the truncated Wiener–Hopf equation. An explicit formula for this relationship is obtained. Note that the matrix-function studied in this paper has not the most General form in Wiener algebra, which is not important in this case. The truncated Wiener–Hopf equation is one of the most studied Fredholm integral equations of the second kind. Therefore, we can expect that the idea of such information will lead to new results in the study of the factorization problem.
Keywords:
truncated Wiener–Hopf equation, Wiener algebra, factorization problem, Riemann boundary value problem, matrix-function, partial indices.
Citation:
A. F. Voronin, “On the relationship between the factorization problem in the Wiener algebra and the truncated Wiener–Hopf equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 12, 22–31; Russian Math. (Iz. VUZ), 64:12 (2020), 20–28
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\by A.~F.~Voronin
\paper On the relationship between the factorization problem in the Wiener algebra and the truncated Wiener--Hopf equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2020
\issue 12
\pages 22--31
\mathnet{http://mi.mathnet.ru/ivm9632}
\crossref{https://doi.org/10.26907/0021-3446-2020-12-22-31}
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\jour Russian Math. (Iz. VUZ)
\yr 2020
\vol 64
\issue 12
\pages 20--28
\crossref{https://doi.org/10.3103/S1066369X20120038}
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Linking options:
https://www.mathnet.ru/eng/ivm9632
https://www.mathnet.ru/eng/ivm/y2020/i12/p22
This publication is cited in the following 7 articles:
A. F. Voronin, “On conditions for the well-posed solvability of a factorization problem and a class of truncated Wiener—Hopf equations”, J. Appl. Industr. Math., 18:3 (2024), 575–582
A. F. Voronin, “Postroenie faktorizatsii odnogo klassa matrits-funktsii v algebre Vinera poryadka dva”, Izv. vuzov. Matem., 2023, no. 3, 41–51
A. F. Voronin, “Factorization of a Class of Matrix Functions in the Wiener Algebra of Order 2”, Russ Math., 67:3 (2023), 32
A. F. Voronin, “K metodu faktorizatsii matrits-funktsii v algebre Vinera poryadka 2”, Sib. zhurn. industr. matem., 25:2 (2022), 32–45
A. F. Voronin, “On a Factorization Method for Matrix Functions in the Wiener Algebra of Order 2”, J. Appl. Ind. Math., 16:2 (2022), 365
A. F. Voronin, “Inhomogeneous vector Riemann boundary value problem and convolutions equation on a finite interval”, Russian Math. (Iz. VUZ), 65:3 (2021), 12–24
A. F. Voronin, “Some questions on the relationship of the factorization problem of matrix functions and the truncated Wiener—Hopf equation in the Wiener algebra”, Sib. elektron. matem. izv., 18:2 (2021), 1615–1624
Citation in format AMSBIB
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