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Integral Equations with Multidimensional Partial Integrals

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We obtain Fredholm criteria for linear equations with multidimensional partial integrals in the space of continuous functions of three variables provided that the kernels are continuous vector-valued functions on a rectangle with the values in spaces of integrable functions. We establish the Fredholm criterion for equations with degenerate kernels and describe the scheme of studying the Fredholm properties of linear equations with partial integrals in spaces of continuous functions of at least four variables.

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Authors and Affiliations

  1. Lipetsk State Pedagogical University, 42, Lenina St, Lipetsk, 398020, Russia

    A. S. Kalitvin, A. I. Inozemtsev & V. A. Kalitvin

Authors
  1. A. S. Kalitvin
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  2. A. I. Inozemtsev
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  3. V. A. Kalitvin
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Corresponding author

Correspondence to V. A. Kalitvin.

Additional information

Translated from Problemy Matematicheskogo Analiza 103, 2020, pp. 125-136.

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Kalitvin, A.S., Inozemtsev, A.I. & Kalitvin, V.A. Integral Equations with Multidimensional Partial Integrals. J Math Sci 249, 954–966 (2020). https://doi.org/10.1007/s10958-020-04987-8

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  • DOI: https://doi.org/10.1007/s10958-020-04987-8

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