APPROXIMATE METHODS FOR SINGULAR INTEGRAL EQUATIONS WITH A NON-CARLEMAN SHIFT

It is known that some problems of synthesis with continuous time and stationary parameters can be reduced to the solution of Wiener-Hopf equations on the semiaxis R+ = [0, ∞). If the problem of synthesis is not stationary, then the Wiener-Hopf method is not applicable. In this case the problem of sy...

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Veröffentlicht in:	The Journal of integral equations and applications 1996, Vol.8 (1), p.1-17
Hauptverfasser:	BATUREV, A.A., KRAVCHENKO, V.G., LITVINCHUK, G.S.
Format:	Artikel
Sprache:	eng
Schlagworte:	Degrees of polynomials Differential equations Geometric translations Linear systems Mathematical integrals Mathematical vectors Polynomials Singular integral equations Solvability
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container_title	The Journal of integral equations and applications
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creator	BATUREV, A.A. KRAVCHENKO, V.G. LITVINCHUK, G.S.
description	It is known that some problems of synthesis with continuous time and stationary parameters can be reduced to the solution of Wiener-Hopf equations on the semiaxis R+ = [0, ∞). If the problem of synthesis is not stationary, then the Wiener-Hopf method is not applicable. In this case the problem of synthesis is reduced to a singular integral equation Tφ = f on the unit circle T with a non-Carleman shift of T onto itself, which has a finite set of fixed points. An estimate for dim ker T is obtained and an approximation algorithm of this estimate is given. For the case dim ker T = 0 we construct an approximate solution of the equation Tφ = f.
doi_str_mv	10.1216/jiea/1181075913
format	Article
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If the problem of synthesis is not stationary, then the Wiener-Hopf method is not applicable. In this case the problem of synthesis is reduced to a singular integral equation Tφ = f on the unit circle T with a non-Carleman shift of T onto itself, which has a finite set of fixed points. An estimate for dim ker T is obtained and an approximation algorithm of this estimate is given. 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If the problem of synthesis is not stationary, then the Wiener-Hopf method is not applicable. In this case the problem of synthesis is reduced to a singular integral equation Tφ = f on the unit circle T with a non-Carleman shift of T onto itself, which has a finite set of fixed points. An estimate for dim ker T is obtained and an approximation algorithm of this estimate is given. For the case dim ker T = 0 we construct an approximate solution of the equation Tφ = f.</abstract><pub>The Rocky Mountain Mathematics Consortium</pub><doi>10.1216/jiea/1181075913</doi><tpages>17</tpages><oa>free_for_read</oa></addata></record>
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source	JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete
subjects	Degrees of polynomials Differential equations Geometric translations Linear systems Mathematical integrals Mathematical vectors Polynomials Singular integral equations Solvability
title	APPROXIMATE METHODS FOR SINGULAR INTEGRAL EQUATIONS WITH A NON-CARLEMAN SHIFT
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