The existence of a generalized fourier transform for a solution as a radiation condition for a class of problems generalizing oscillation excitation problems in regular waveguides

  • A. N. Bogolyubov
  • M. D. Malykh
  • Yu. V. MukhartovaEmail author


For a second-order inhomogeneous differential equation defined on the real axis and such that its right-hand side and solutions are functions in a Hilbert space, it is shown that the existence of a generalized Fourier transform of the solution is a correct radiation condition if the right-hand side is sufficiently smooth and compactly supported.


generalized Fourier transform non-self-adjoint operator bundle radiation condition regular waveguide theory 


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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • A. N. Bogolyubov
    • 1
  • M. D. Malykh
    • 1
  • Yu. V. Mukhartova
    • 1
    Email author
  1. 1.Faculty of PhysicsMoscow State UniversityMoscowRussia

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