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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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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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\jour Math. USSR-Sb.
\yr 1991
\vol 70
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\pages 205--230
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http://mi.mathnet.ru/eng/msb1142 http://mi.mathnet.ru/eng/msb/v181/i6/p779
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This publication is cited in the following articles:
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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
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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
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