Geodesic
On Some Properties of Systems
Matematičeskie zametki, Tome 80 (2006) no. 1, pp. 115-118 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the system of integral equations of the form $Ax+Vx=\nobreak \psi$, where $V$ is the Volterra operator with kernel of convolution type and $A$ is a constant matrix, $\det A=\nobreak 0$. We prove an existence theorem and establish necessary and sufficient conditions for the kernel of the operator of the system to be trivial.
Keywords: Volterra integral equation, left regularizing operator, Fredholm operator, integro-differential operator.
Mots-clés : convolution-type kernel 
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V. F. Chistyakov. On Some Properties of Systems. Matematičeskie zametki, Tome 80 (2006) no. 1, pp. 115-118. http://geodesic.mathdoc.fr/item/MZM_2006_80_1_a13/

[1] M. S. Nikolskii, “O sistemakh lineinykh integralnykh uravnenii tipa Volterra v svertkakh”, Tr. MIRAN im. V. A. Steklova, 220, 1998, 210–216

[2] V. F. Chistyakov, “O razreshimosti sistem integralnykh uravnenii Volterra 4 roda. I”, Differents. uravneniya, 38:5 (2002), 698–707 | MR | Zbl

[3] M. L. Krasnov, Integralnye uravneniya, Nauka, M., 1975 | MR | Zbl

[4] N. N. Luzin, “K izucheniyu matrichnoi sistemy teorii differentsialnykh uravnenii”, Avtomatika i telemekhanika, 1940, no. 5, 4–66 | MR | Zbl