Siberian Mathematical Journal

, Volume 56, Issue 3, pp 435–441 | Cite as

On systems of linear functional equations of the third kind in L 2

  • V. B. KorotkovEmail author


We consider the systems of linear functional equations of the third kind with measurecompact operators in L 2 and the general systems of linear integral equations of the third kind in L 2. We propose a method for reducing these systems either to equivalent integral equations of the first kind with nuclear operators or to equivalent integral equations of the second kind with quasidegenerate Carleman kernels. Various exact and approximate methods for solving the arising integral equations are applicable.


system of linear functional equations of the third kind measure-compact operator integral operator integral equation of the first or second kind nuclear operator quasidegenerate Carleman kernel 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Birman M. Sh., Vilenkin N. Ya., Gorin E. A. et al., Functional Analysis [in Russian], Nauka, Moscow (1972).Google Scholar
  2. 2.
    Gantmakher F. R., The Theory of Matrices [in Russian], Nauka, Moscow (1967).Google Scholar
  3. 3.
    Korotkov V. B., Integral Operators [in Russian], Nauka, Novosibirsk (1983).Google Scholar
  4. 4.
    Korotkov V. B., “Linear functional equations of the first, second, and third kind in L 2,” Siberian Math. J., 54, No. 6, 1029–1036 (2013).zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Korotkov V. B. and Stepanov V. D., “On some properties of integral convolution operators,” in: Applications of the Methods of Functional Analysis to the Problems of Mathematical Physics and Computational Mathematics [in Russian], Nauka, Novosibirsk, 1979, pp. 64–68.Google Scholar
  6. 6.
    Korotkov V. B., “Regular and compact factorization of integral operators in L p,” Math. Notes, 32, No. 5, 785–788 (1982).MathSciNetCrossRefGoogle Scholar
  7. 7.
    Schachermayer W. and Weis L., “Almost compactness and decomposability of integral operators,” Proc. Amer. Math. Soc., 81, No. 4, 595–599 (1981).zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Korotkov V. B., “Reducing certain operator families to integral form,” Siberian Math. J., 34, No. 3, 481–485 (1993).MathSciNetCrossRefGoogle Scholar
  9. 9.
    Korotkov V. B., “A method of solving integral equations with arbitrary kernels,” Siberian Math. J., 28, No. 1, 89–92 (1987).zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Korotkov V. B., Some Topics in the Theory of Integral Operators [in Russian], Inst. Mat., Novosibirsk (1988).Google Scholar
  11. 11.
    Novitskiĭ I. M., “A kernel smoothing method for general integral equations,” Dalnevost. Mat. Zh., 12, No. 2, 255–261 (2012).zbMATHMathSciNetGoogle Scholar
  12. 12.
    Korotkov V. B., “Systems of integral equations,” Siberian Math. J., 27, No. 3, 406–416 (1986).zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

Personalised recommendations