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Necessary and sufficient well-posedness conditions for a convolution equation of the second kind with even kernel on a finite interval

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Abstract

We derive some necessary and sufficient conditions for the well-posedness of a convolution equation of the second kind with even kernel on a finite interval. In order to check these conditions it suffices to compute a one-dimensional integral (of a given function) with precision less than 0.5. As an intermediate result we give a strengthening of the Fredholm alternative for the equation in question with an arbitrary kernel in L 1.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. F. Voronin

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  1. A. F. Voronin
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Correspondence to A. F. Voronin.

Additional information

Original Russian Text Copyright © 2008 Voronin A. F.

The author was partially supported by the Russian Foundation for Basic Research (Grant 06-01-00422), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-1440.2008.1), and the Interdisciplinary Integration Grants (No. 3 and No. 48; 2006) of the Siberian Division of the Russian Academy of Sciences.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 4, pp. 756–767, July–August, 2008.

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Voronin, A.F. Necessary and sufficient well-posedness conditions for a convolution equation of the second kind with even kernel on a finite interval. Sib Math J 49, 601–611 (2008). https://doi.org/10.1007/s11202-008-0057-1

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  • DOI: https://doi.org/10.1007/s11202-008-0057-1

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