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Mat. Sb., 1990, Volume 181, Number 6, Pages 779–803 (Mi msb1142)  

This article is cited in 2 scientific papers (total in 2 papers)

The Wiener–Hopf equation and Blaschke products

V. B. Dybin

Rostov State University

Abstract: A Wiener–Hopf operator $A$ is studied in the space of functions locally square-integrable on $\mathbf R$ and slowly increasing to $\infty$. The symbol of the operator is an infinitely differentiable function on $\mathbf R$ and has at $\infty$ a discontinuity of “vorticity point” type described either by a Blaschke function with all its zeros concentrated in a strip and bounded away from $\mathbf R$, or by an outer function meromorphic in the complex plane with separated set of real zeros of bounded multiplicity. The operator $A$ is one-sidedly invertible, and $\operatorname{ind}A=\pm\infty$. Procedures are worked out for inverting it. The subspace $\operatorname{ker}A$ is described in terms of generalized Dirichlet series.

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English version:
Mathematics of the USSR-Sbornik, 1991, 70:1, 205–230

Bibliographic databases:

UDC: 517.5
MSC: Primary 45E10, 47B35, 30D50; Secondary 30B50
Received: 27.06.1987 and 04.12.1989

Citation: V. B. Dybin, “The Wiener–Hopf equation and Blaschke products”, Mat. Sb., 181:6 (1990), 779–803; Math. USSR-Sb., 70:1 (1991), 205–230

Citation in format AMSBIB
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\paper The Wiener--Hopf equation and Blaschke products
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\yr 1990
\vol 181
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\pages 779--803
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\transl
\jour Math. USSR-Sb.
\yr 1991
\vol 70
\issue 1
\pages 205--230
\crossref{https://doi.org/10.1070/SM1991v070n01ABEH001938}
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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. Dybin V.B., “Uravnenie svërtki na veschestvennoi pryamoi v prostranstve funktsii, summiruemykh s eksponentsialnymi vesami. chast 1”, Vestnik rossiiskogo universiteta druzhby narodov. seriya: matematika, informatika, fizika, 2011, no. 2, 16–27  elib
    2. V. B. Dybin, S. B. Dzhirgalova, “Scalar Discrete Convolutions in Spaces of Sequences Summed with Exponential Weights—Part 1: One-Sided Invertibility”, Integr. Equ. Oper. Theory, 2014  crossref
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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