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Siberian Mathematical Journal

, Volume 44, Issue 5, pp 829–832 | Cite as

On the Integral Operators of the Third Kind

  • V. B. Korotkov
Article

Abstract

We establish some necessary and sufficient conditions for an operator in the space of square summable functions to be representable as a sum of multiplication by a bounded function and an integral operator.

multiplication by a function integral operator kernel of an integral operator integral operator of the third kind 

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References

  1. 1.
    Halmos P. R. and Sunder V. S., Bounded Integral Operators on L 2 Spaces [Russian translation], Nauka, Moscow (1985).Google Scholar
  2. 2.
    Bukhvalov A. V., “Applications of the methods of the theory of order bounded operators to the theory of operators in the Lpspaces,” Uspekhi Mat. Nauk, 38, No. 6, 37–83 (1983).Google Scholar
  3. 3.
    Nikishin E. M., “Resonance theorems and sublinear operators,” Uspekhi Mat. Nauk, 25, No. 6, 129–191 (1970).Google Scholar
  4. 4.
    Korotkov V. B., Integral Operators [in Russian], Nauka, Novosibirsk (1983).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • V. B. Korotkov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirsk

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