We study the Fredholm property of linear equations with partial integrals and kernels in some classes. We show that a linear operator with partial integrals acts in the space of integrable functions and in the space of continuous functions defined in a square. We give an example of a non-Fredholm homogeneous linear equation of the second kind with partial integrals and continuous kernels. We obtain Fredholm criteria for linear operators and equations with partial integrals in the space of integrable functions. Bibliography: 6 titles.
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Translated from Problemy Matematicheskogo Analiza 103, 2020, pp. 137-142.
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Kalitvin, V.A. Fredholm Property of Linear Equations with Partial Integrals in the Space of Integrable Functions. J Math Sci 249, 967–973 (2020). https://doi.org/10.1007/s10958-020-04988-7
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DOI: https://doi.org/10.1007/s10958-020-04988-7