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Mat. Sb., 2009, Volume 200, Number 8, Pages 3–24 (Mi msb6360)  

This article is cited in 9 scientific papers (total in 9 papers)

Wiener-Hopf factorization of piecewise meromorphic matrix-valued functions

V. M. Adukov

South Ural State University

Abstract: Let $\mathrm D^+$ be a multiply connected domain bounded by a contour $\Gamma$, let $\mathrm D^-$ be the complement of $\mathrm D^+\cup\Gamma$ in $\overline{\mathbb C}={\mathbb C}\cup\{\infty\}$, and $a(t)$ be a continuous invertible matrix-valued function on $\Gamma$ which can be meromorphically extended into the open disconnected set $\mathrm D^-$ (as a piecewise meromorphic matrix-valued function). An explicit solution of the Wiener-Hopf factorization problem for $a(t)$ is obtained and the partial factorization indices of $a(t)$ are calculated. Here an explicit solution of a factorization problem is meant in the sense of reducing it to the investigation of finitely many systems of linear algebraic equations with matrices expressed in closed form, that is, in quadratures.
Bibliography: 15 titles.

Keywords: Wiener-Hopf factorization of matrix-valued functions, Riemann boundary-value problem, partial indices.

DOI: https://doi.org/10.4213/sm6360

Full text: PDF file (554 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:8, 1105–1126

Bibliographic databases:

UDC: 517.544.8
MSC: Primary 47A68, 30E25; Secondary 47A56, 35Q15
Received: 13.05.2008

Citation: V. M. Adukov, “Wiener-Hopf factorization of piecewise meromorphic matrix-valued functions”, Mat. Sb., 200:8 (2009), 3–24; Sb. Math., 200:8 (2009), 1105–1126

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Adukov V.M., Patrushev A.A., “Algoritm tochnogo resheniya chetyrekhelementnoi zadachi lineinogo sopryazheniya s ratsionalnymi koeffitsientami i ego programmnaya realizatsiya”, Vestn. Yuzhno-Uralskogo gos. un-ta. Ser.: Matematicheskoe modelirovanie i programmirovanie, 2010, no. 35, 4–11  zmath  elib
    2. V. M. Adukov, A. A. Patrushev, “Algoritm tochnogo resheniya chetyrekhelementnoi zadachi lineinogo sopryazheniya s ratsionalnymi koeffitsientami i ego programmnaya realizatsiya”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2010, no. 6, 4–11  mathnet
    3. V. M. Adukov, A. A. Patrushev, “O yavnom i tochnom resheniyakh zadachi Markushevicha na okruzhnosti”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 11:2 (2011), 9–20  mathnet  elib
    4. V. M. Adukov, “O zadache minimalnoi realizatsii”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 6:3 (2013), 5–17  mathnet
    5. V. M. Adukov, “O faktorizatsii Vinera–Khopfa funktsionalno-kommutativnykh matrits-funktsii”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 5:2 (2013), 6–12  mathnet
    6. V. M. Adukov, A. A. Patrushev, “Odin iz sluchaev trekhelementnoi kraevoi zadachi lineinogo sopryazheniya na pryamoi”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 6:1 (2014), 5–9  mathnet
    7. A. G. Kamalian, “A Factorization Method for Products of Holomorphic Matrix Functions”, Math. Notes, 100:2 (2016), 213–228  mathnet  crossref  crossref  mathscinet  isi  elib
    8. S. N. Kiyasov, “Method of solving linear conjugation problem for two-dimensional vector for known partial solution”, Russian Math. (Iz. VUZ), 60:11 (2016), 1–10  mathnet  crossref  isi
    9. Rogosin S., Mishuris G., “Constructive methods for factorization of matrix-functions”, IMA J. Appl. Math., 81:2 (2016), 365–391  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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