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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 4, Pages 756–767 (Mi smj1875)  
This article is cited in 7 scientific papers (total in 7 papers)

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

A. F. Voronin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (316 kB) Citations (7)
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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 $L_1$.
Keywords: integral equation, convolution, interval, well-posedness, Fredholm alternative, Riemann problem.
Received: 13.04.2006
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 4, Pages 601–611
DOI: https://doi.org/10.1007/s11202-008-0057-1
Bibliographic databases:
UDC: 517.968
Language: Russian
Citation: A. F. Voronin, “Necessary and sufficient well-posedness conditions for a convolution equation of the second kind with even kernel on a finite interval”, Sibirsk. Mat. Zh., 49:4 (2008), 756–767; Siberian Math. J., 49:4 (2008), 601–611
Citation in format AMSBIB
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\pages 756--767
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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