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Factorization of a Class of Matrix Functions in the Wiener Algebra of Order 2

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Abstract

A representative class of matrix functions from the Wiener algebra of order 2 admitting an effective factorization is found. The factorization problem for elements of this class is reduced to a truncated Wiener–Hopf equation with a contracting integral operator. The latter guarantees, as will be shown in the article, the existence of a canonical factorization and its explicit construction for matrix functions from the class under consideration.

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REFERENCES

  1. A. Voronin, “Some questions on the relationship of the factorization problem of matrix functions and the truncated Wiener–Hopf equation in the Wiener algebra,” Sibirskie Elektronnye Mat. Izv. 18, 1615–1624 (2021). https://doi.org/10.33048/semi.2021.18.119

    Article  MathSciNet  MATH  Google Scholar 

  2. A. F. Voronin, “Inhomogeneous vector Riemann boundary value problem and convolutions equation on a finite interval,” Russ. Math. 65, 12–24 (2021). https://doi.org/10.3103/S1066369X21030026

    Article  MATH  Google Scholar 

  3. A. F. Voronin, “On the relationship between the factorization problem in the Wiener algebra and the truncated Wiener–Hopf equation,” Russ. Math. 64, 20–28 (2020). https://doi.org/10.3103/S1066369X20120038

    Article  MathSciNet  MATH  Google Scholar 

  4. A. F. Voronin, “On a factorization method for matrix functions in the Wiener algebra of order 2,” J. Appl. Ind. Math. 16, 365–376 (2022). https://doi.org/10.1134/S1990478922020168

    Article  MathSciNet  Google Scholar 

  5. N. I. Muskhelishvili, Singular Integral Equations (Nauka, Moscow, 1968).

    MATH  Google Scholar 

  6. A. F. Voronin, “On ℝ-linear problem and truncated Wiener–Hopf equation,” Sib. Adv. Math. 30, 143–151 (2019). https://doi.org/10.3103/S1055134420020066

    Article  MathSciNet  Google Scholar 

  7. P. P. Zabreiko, A. I. Koshelev, M. A. Krasnosel’skii, S. G. Mikhlin, L. S. Rakovshchik, and V. Ya. Stetsenko, Integral Equations (Nauka, Moscow, 1968).

    MATH  Google Scholar 

  8. I. Ts. Gokhberg and M. G. Krein, “Systems of integral equations on the half-line with kernels depending on the difference of the arguments,” Usp. Mat. Nauk 13 (2), 3–72 (1958).

    MathSciNet  Google Scholar 

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Funding

This work was supported by the State Task of the Institute of Mathematics of the Siberian Branch, Russian Academy of Sciences, project no. FWNF-2022-0009.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    A. F. Voronin

  2. Novosibirsk State Technical University, 630073, Novosibirsk, Russia

    A. F. Voronin

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  1. A. F. Voronin
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Correspondence to A. F. Voronin.

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The author declares that he has no conflicts of interest.

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Translated by O. Pismenov

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Voronin, A.F. Factorization of a Class of Matrix Functions in the Wiener Algebra of Order 2. Russ Math. 67, 32–41 (2023). https://doi.org/10.3103/S1066369X23030076

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  • DOI: https://doi.org/10.3103/S1066369X23030076

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