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

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Abstract

We consider a general system of functional equations of the second kind in L 2 with a continuous linear operator T satisfying the condition that zero lies in the limit spectrum of the adjoint operator T*. We show that this condition holds for the operators of a wide class containing, in particular, all integral operators. The system under study is reduced by means of a unitary transformation to an equivalent system of linear integral equations of the second kind in L 2 with Carleman matrix kernel of a special kind. By a linear continuous invertible change, this system is reduced to an equivalent integral equation of the second kind in L 2 with quasidegenerate Carleman kernel. It is possible to apply various approximate methods of solution for such an equation.

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References

  1. Krasnosel′skiĭ M. A. et al., Integral Operators in Spaces of Summable Functions, Noordhoff Intern. Publ., Leyden (1976).

    Book  Google Scholar 

  2. Korotkov V. B., Integral Operators [Russian], Nauka, Novosibirsk (1983).

    MATH  Google Scholar 

  3. Korotkov V. B., Some Topics in the Theory of Integral Operators [Russian], Inst. Mat., Novosibirsk (1988).

    MATH  Google Scholar 

  4. Misra B., Speiser D., and Targonski G., “Integral operators in the theory of scattering,” Helv. Phys. Acta, vol. 36, no. 7, 963–980 (1963).

    MATH  MathSciNet  Google Scholar 

  5. Korotkov V. B., “On the nonintegrality property of the Fredholm resolvent of some integral operators,” Sib. Math. J., vol. 39, no. 4, 781–783 (1998).

    Article  Google Scholar 

  6. Korotkov V. B., An Introduction to the Algebraic Theory of Integral Operators [Russian], Kolorit, Vladivostok (2000).

    Google Scholar 

  7. Novitskiĭ I. M., “Some properties of the resolvent kernels for integral equations with bi-Carleman kernels,” Dalnevost. Mat. Zh., vol. 16, no. 2, 186–208 (2016).

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    V. B. Korotkov

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  1. V. B. Korotkov
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Correspondence to V. B. Korotkov.

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Original Russian Text Copyright © 2017 Korotkov V.B.

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 5, pp. 1091–1097, September–October, 2017; DOI: 10.17377/smzh.2017.58.511.

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Korotkov, V.B. On systems of linear functional equations of the second kind in L 2 . Sib Math J 58, 845–849 (2017). https://doi.org/10.1134/S0037446617050111

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  • DOI: https://doi.org/10.1134/S0037446617050111

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