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On Compactness of Regular Integral Operators in the Space L1

  • Differential and Integral Equations
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Abstract

In this paper we obtain a sufficient condition for quite continuity of Fredholm type integral operators in the space L1(a, b). Uniform approximations by operators with degenerate kernels of horizontally striped structures are constructed. A quantitative error estimate is obtained. We point out the possibility of application of the obtained results to second kind integral equations, including convolution equations on a finite interval, equations with polar kernels, one-dimensional equations with potential type kernels, and some transport equations in non-homogeneous layers.

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Authors and Affiliations

  1. Institute of Mathematics of NAS RA, Yerevan, Armenia

    B. N. Yengibaryan & N. B. Yengibaryan

Authors
  1. B. N. Yengibaryan
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  2. N. B. Yengibaryan
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Correspondence to B. N. Yengibaryan.

Additional information

Original Russian Text © B. N. Yengibaryan, N. B. Yengibaryan, 2018, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2018, No. 6, pp. 46–52.

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Yengibaryan, B.N., Yengibaryan, N.B. On Compactness of Regular Integral Operators in the Space L1. J. Contemp. Mathemat. Anal. 53, 317–320 (2018). https://doi.org/10.3103/S106836231806002X

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  • DOI: https://doi.org/10.3103/S106836231806002X

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