Geodesic
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
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 293-300

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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. 
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     author = {A. N. Bogolyubov and M. D. Malykh and Yu. V. Mukhartova},
     title = {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},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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A. N. Bogolyubov; M. D. Malykh; Yu. V. Mukhartova. 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. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 293-300. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a7/