Abstract:
We consider linear operators and equations with partial integrals in Banach ideal spaces, spaces of vector functions, and spaces of continuous functions. We study the action, regularity, duality, algebras, Fredholm properties, invertibility, and spectral properties of such operators. We describe principal properties of linear equations with partial integrals. We show that such equations are essentially different compared to usual integral equations. We obtain conditions for the Fredholm alternative, conditions for zero spectral radius of the Volterra operator with partial integrals, and construct resolvents of invertible equations. We discuss Volterra–Fredholm equations with partial integrals and consider problems leading to linear equations with partial integrals.
Document Type:
Article
UDC:517.968
Language: Russian
Citation:
A. S. Kalitvin, V. A. Kalitvin, “Linear operators and equations with partial integrals”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 65, no. 3, PFUR, M., 2019, 390–433
\Bibitem{KalKal19}
\by A.~S.~Kalitvin, V.~A.~Kalitvin
\paper Linear operators and equations with partial integrals
\inbook Proceedings of the Crimean autumn mathematical school-symposium
\serial CMFD
\yr 2019
\vol 65
\issue 3
\pages 390--433
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd384}
\crossref{https://doi.org/10.22363/2413-3639-2019-65-3-390-433}
Linking options:
https://www.mathnet.ru/eng/cmfd384
https://www.mathnet.ru/eng/cmfd/v65/i3/p390
This publication is cited in the following 2 articles:
D. Zh. Kulturaev, Yu. Kh. Eshkabilov, “On the Spectral Properties of Selfadjoint Partial Integral Operators with a Nondegenerate Kernel”, Sib Math J, 65:2 (2024), 475
A. D. Arziev, K. K. Kudaybergenov, P. R. Oryinbaev, A. K. Tanirbergen, “Partial Integral Operators on Banach–Kantorovich Spaces”, Math. Notes, 114:1 (2023), 15–29
Citation in format AMSBIB
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