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Mathematical Notes

, Volume 63, Issue 3, pp 302–310 | Cite as

A geometric method for solving a series of integral Poincaré-Steklov equations

  • A. B. Bogatyre
Article

Abstract

Eigenvalues and eigenfunctions are explicitly found for a family of singular integral equations. It is shown how their discrete spectrum becomes continuous as the equation degenerates.

Key words

Poincaré-Steklov equation integral equation spectrum discrete spectrum singular integral equation 

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References

  1. 1.
    A. B. Bogatyrev, “On spectra of pairs of Poincaré-Steklov operators,”Russian J. Numer. Anal. Math. Modelling,8, No. 3, 171–194 (1993).MathSciNetGoogle Scholar
  2. 2.
    A. B. Bogatyrev, “Discrete spectrum of the problem for a pair of Poincaré-Steklov operators,”Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.],358, No. 3 (1998).Google Scholar
  3. 3.
    V. I. Lebedev and V. I. Agoshkov,Poincaré-Steklov Operators and Their Applications in Analysis [in Russian], Division of Computational Mathematics, Russian Academy of Sciences, Moscow (1983).Google Scholar
  4. 4.
    P. Grisvard,Elliptic Problems in Nonsmooth Domains, Pitman, Boston (1985).Google Scholar
  5. 5.
    J.-L. Lions and B. Magenes,Problèmes aux limites non homogènes et applications, Dunod, Paris (1968).Google Scholar
  6. 6.
    É. E. Ovchinnikov, “Adjoint equations, perturbation algorithms, and optimal control,” in:Collection of Scientific Papers (V. I. Agoshkov and V. P. Shutyaev, editors) [in Russian], VINITI, Moscow (1993), pp. 64–100 (Dep. VINITI No. 453-B93, 25.03.93).Google Scholar
  7. 7.
    F. D. Gakhov and L. I. Chibrikova, “On some types of singular integral equations solvable in a closed form,”Mat. Sb. [Math. USSR-Sb.],35, No. 3, 395–491 (1954).MathSciNetGoogle Scholar
  8. 8.
    F. D. Gakhov,Boundary Value Problems [in Russian], Nauka, Moscow (1978).Google Scholar
  9. 9.
    N. I. Muskhelishvili,Singular Integral Equations [in Russian], Nauka, Moscow (1968).Google Scholar
  10. 10.
    I. I. Privalov,Boundary Properties of Analytic Functions [in Russian], Gostekhizdat, Moscow (1950).Google Scholar
  11. 11.
    M. A. Lavrent'ev and B. V. Shabat,Methods of Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • A. B. Bogatyre
    • 1
  1. 1.Institute for Computational MathematicsRussian Academy of SciencesUSSR

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