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 Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 4, Pages 767–784 (Mi izv1318)

The Wiener–Hopf equation in Nevanlinna and Smirnov algebras

Abstract: A generalized Wiener–Hopf equation on the semiaxis is considered in the class of analytic functionals which are the Fourier transform of Nevanlinna algebras $N^\pm$ or Smirnov algebras $N_*^\pm$. The problem, connected with this equation, of factoring measurable functions $\rho(x)$ on the axis in the algebras $N_*^\pm$ which satisfy the condition $(1+x^2)^{-1}\ln|\rho(x)|\in \mathscr L_1(-\infty,\infty)$ and also the problem of linear junction $\rho\varphi^+=\psi^-+F^+$ in the algebras $N^\pm$ and $N_*^\pm$ are also considered.
Bibliography: 24 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1988, 31:1, 77–94

Bibliographic databases:

UDC: 517.54+517.96
MSC: Primary 45E10; Secondary 46F15

Citation: V. S. Vladimirov, “The Wiener–Hopf equation in Nevanlinna and Smirnov algebras”, Izv. Akad. Nauk SSSR Ser. Mat., 51:4 (1987), 767–784; Math. USSR-Izv., 31:1 (1988), 77–94

Citation in format AMSBIB
\Bibitem{Vla87} \by V.~S.~Vladimirov \paper The Wiener--Hopf equation in Nevanlinna and Smirnov algebras \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1987 \vol 51 \issue 4 \pages 767--784 \mathnet{http://mi.mathnet.ru/izv1318} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=914859} \zmath{https://zbmath.org/?q=an:0653.45004|0635.45004} \transl \jour Math. USSR-Izv. \yr 1988 \vol 31 \issue 1 \pages 77--94 \crossref{https://doi.org/10.1070/IM1988v031n01ABEH001044} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. B. Dybin, “The Wiener–Hopf equation and Blaschke products”, Math. USSR-Sb., 70:1 (1991), 205–230
2. A. A. Gonchar, G. I. Marchuk, S. P. Novikov, “Vasilii Sergeevich Vladimirov (on his seventieth birthday)”, Russian Math. Surveys, 48:1 (1993), 201–212
3. N. B. Engibaryan, “Convolution equations containing singular probability distributions”, Izv. Math., 60:2 (1996), 249–280
4. M. K. Kerimov, “Vasiliĭ Sergeevich Vladimirov (on the occasion of his eightieth birthday)”, Comput. Math. Math. Phys., 43:11 (2003), 1541–1549
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