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S.M. Belotserkovskii, I.K. Lifanov (1985)
Chislennye metody v singulyarnykh integral’nykh uravneniyakh i ikh primenenie v aerodinamike, teorii uprugosti, elektrodinamike
M. Golberg (1979)
Solution Methods for Integral Equations
I.K. Lifanov, E.E. Tyrtyshnikov (1990)
Vychislit. protsessy i sistemy
V.V. Ivanov (1968)
Teoriya priblizhennykh metodov i ee primenenie k chislennomu resheniyu singulyarnykh integral’nykh uravnenii
E. Titchmarsh (1938)
Introduction to the Theory of Fourier Integrals
I.K. Lifanov (1995)
Metod singulyarnykh integral’nykh uravnenii i chislennyi eksperiment
S.G. Mikhlin (1970)
Variatsionnye metody v matematicheskoi fizike
F.D. Gakhov (1977)
Kraevye zadachi
H. Gajewski, K. Gröger, K. Zacharias (1974)
Nichtlineare Operatorgleichungen und OperatordifferentialgleichungenMathematische Nachrichten, 67
S.G. Michlin, S. Prößdorf (1980)
Singuläre Integraloperatoren
B.G. Gabdulkhaev (1995)
Chislennyi analiz singulyarnykh integral’nykh uravnenii. Izbrannye glavy
B.G. Gabdulkhaev (1980)
Optimal’nye approksimatsii reshenii lineinykh zadach
A.V. Kantorovich, G.P. Akilov (1984)
Funktsional’nyi analiz
B.G. Gabdulkhaev (1980)
Itogi Nauki Tekh. Mat. Anal.
D. Elliott (1979)
The Approximate Solution of Singular Integral Equations
We study exact and approximate methods for solving a singular integral equation with Cauchy kernel on the real line. On the basis of the theory of positive operators, we prove an existence and uniqueness theorem for this equation in the space of Lebesgue square integrable functions. This theorem is then used to give a theoretical justification of general projection and projection-iteration methods as well as an iteration method for solving this equation.
Differential Equations – Springer Journals
Published: Sep 27, 2008
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