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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Ilinskii A. C., Kravtsov V. V., Sveshnikov A. G., Matematicheskie modeli elektrodinamiki, Izd-vo MGU, M., 1993

[2] Sveshnikov A. G., “Printsip izlucheniya”, Dokl. AN SSSR, 73:3 (1950), 917–920 | Zbl

[3] Tikhonov A. N., Samarskii A. A., “O vozbuzhdenii radiovolnovodov. I”, Zh. tekhn. fiz., 17:11 (1947), 1283–1296

[4] Tikhonov A. N., Samarskii A. A., “O vozbuzhdenii radiovolnovodov. II”, Zh. tekhn. fiz., 17:12 (1947), 1431–1440

[5] Tikhonov A. N., Samarskii A. A., “O predstavlenii polya v volnovode v vide summy polei TE i TM”, Zh. tekhn. fiz., 18:7 (1948), 959–970

[6] Krasnushkin P. E., Moiseev E. I., “O vozbuzhdenii vynuzhdennykh kolebanii v sloistom radiovolnovode”, Dokl. AN SSSR, 264:5 (1982), 1123–1127 | MR

[7] Veselov G. I., Krasnushkin P. E., “O dispersionnykh svoistvakh dvukhsloinogo ekranirovannogo kruglogo volnovoda i kompleksnykh volnakh v nem”, Dokl. AN SSSR, 260:3 (1981), 576–579 | MR

[8] Smirnov Yu. G., “O polnote sistemy sobstvennykh i prisoedinennykh voln chastichno zapolnennogo volnovoda s neregulyarnoi granitsei”, Dokl. AN SSSR, 297:4 (1987), 829–832

[9] Smirnov Yu. G., “Metod operatornykh puchkov v kraevykh zadachakh sopryazheniya dlya sistemy ellipticheskikh uravnenii”, Differents. ur-niya, 27:1 (1991), 140–147 | MR | Zbl

[10] Smirnov Yu. G., “Primenenie metoda operatornykh puchkov v zadache o sobstvennykh volnakh chastichno zapolnennogo volnovoda”, Dokl. RAN, 312:3 (1990), 597–599

[11] Bogolyubov A. N., Delitsyn A. L., Sveshnikov A. G., “O polnote kornevykh vektorov radiovolnovoda”, Dokl. AN, 369:4 (1999), 458–460 | MR

[12] Bogolyubov A. N., Delitsyn A. L., Sveshnikov A. G., “Ob usloviyakh razreshimosti zadachi vozbuzhdeniya radiovolnovoda”, Dokl. RAN, 370:4 (2000), 453–456 | MR

[13] Bogolyubov A. N., Delitsyn A. L., Sveshnikov A. G., “O zadache vozbuzhdeniya volnovoda s neodnorodnym zapolneniem”, Zh. vychisl. matem. i matem. fiz., 39:11 (1999), 1869–1888 | MR | Zbl

[14] Bogolyubov A. N., Malykh M. D., “Zamechanie ob usloviyakh izlucheniya dlya neregulyarnogo volnovoda”, Zh. vychisl. matem. i matem. fiz., 43:4 (2003), 585–588 | MR | Zbl

[15] Bogolyubov A. N., Malykh M. D., Mukhartova Yu. V., “Ob udovletvoryayuschem usloviyu izlucheniya reshenii kraevoi zadachi dlya proizvolnogo ellipticheskogo operatora”, Zh. vychisl. matem. i matem. fiz., 46:12 (2006), 2228–2234 | MR

[16] Keldysh M. V., “O polnote sobstvennykh funktsii nekotorykh klassov nesamosopryazhennykh lineinykh operatorov”, Izbr. trudy. Matematika, Gl. I, Nauka, M., 1985, 305–320

[17] Reshetnyak Yu. G., Kurs matematicheskogo analiza. Ch. 2. Kn. 2. Integralnoe ischislenie funktsii mnogikh peremennykh. Integralnoe ischislenie na mnogoobraziyakh. Vneshnie differentsialnye formy, Izd-vo In-ta matem. SO RAN, Novosibirsk, 2001