On the Poles of an Acoustic Resonator
Funkcionalʹnyj analiz i ego priloženiâ, Tome 27 (1993) no. 4, pp. 3-16.

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R. R. Gadyl'shin. On the Poles of an Acoustic Resonator. Funkcionalʹnyj analiz i ego priloženiâ, Tome 27 (1993) no. 4, pp. 3-16. http://geodesic.mathdoc.fr/item/FAA_1993_27_4_a1/

[1] Rayleigh O. M., “The theory of Helmholtz resonator”, Proc. Roy. Soc. A, 92:638 (1916), 265–275 | DOI | Zbl

[2] Miles J. W., “Scattering by a spherical cap”, J. Acoust. Soc. Amer., 50:3 (1971), 892–903, Pt. 2 | DOI | MR

[3] Babich V. M., “Ob analiticheskom prodolzhenii rezolventy vneshnikh trekhmernykh zadach dlya operatora Laplasa na vtoroi list”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, no. 3, Izd-vo Kharkovskogo universiteta, Kharkov, 1966, 151–157

[4] Laks P., Fillips R., Teoriya rasseyaniya, Mir, M., 1971 | MR

[5] Goldstein C. G., “Scattering theory for elliptic differential operators in unbounded domains”, J. Math. Anal. Appl., 45 (1974), 723–745 | DOI | MR

[6] Gadylshin R. R., “Ob amplitude kolebanii dlya rezonatora Gelmgoltsa”, DAN SSSR, 310:5 (1990), 1094–1097 | MR

[7] Gadylshin R. R., “Poverkhnostnye potentsialy i metod soglasovaniya asimptoticheskikh razlozhenii v zadache o rezonatore Gelmgoltsa”, Algebra i analiz, 4:2 (1992), 88–115 | MR

[8] Arsenev A. A., “Ob osobennostyakh analiticheskogo prodolzheniya i rezonansnykh svoistvakh resheniya zadachi rasseyaniya dlya uravneniya Gelmgoltsa”, Zh. vych. mat. i mat. fiz., 12:1 (1972), 112–138 | MR

[9] Beale J. T., “Scattering Frequencies of Resonators”, Comm. Pure Appl. Math., 26:4 (1973), 549–564 | DOI | MR

[10] Petras S. V., “O rasscheplenii serii rezonansov na nefizicheskom liste”, Funkts. analiz i ego pril., 9:2 (1975), 89–90 | MR | Zbl

[11] Petras S. V., “O rasscheplenii serii rezonansov na nefizicheskom liste”, Zap. nauch. sem. LOMI. – 1975. – T. 51. – S. 155–169.

[12] Arsenev A. A., “O suschestvovanii rezonansnykh polyusov i rezonansov pri rasseyanii v sluchae kraevykh uslovii II i III roda”, Zh. vych. mat. i mat. fiz., 16:3 (1976), 718–724 | MR

[13] Sanches-Palensia E., Neodnorodnye sredy i teoriya kolebanii, Mir, M., 1984 | MR

[14] Fernandez C. A., “Resonances in scattering by a resonator”, Indiana Univ. Math. J., 34:1 (1985), 115–125 | DOI | MR | Zbl

[15] Hislop P. D., Martinez A., “Scattering resonances of a Helmholtz resonator”, Indiana Univ. Math. J., 40:2 (1991), 767–788 | DOI | MR | Zbl

[16] Van Daik M., Metody vozmuschenii v mekhanike zhidkosti, Mir, M., 1967 | Zbl

[17] Naife A., Metody vozmuschenii, Mir, M., 1976 | MR

[18] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR

[19] Mazya V. G., Nazarov S. A., Plamenevskii B. A., “Asimptoticheskie razlozheniya sobstvennykh chisel kraevykh zadach dlya operatora Laplasa v oblastyakh s malymi otverstiyami”, Izv. AN SSSR. Ser. mat., 48:2 (1984), 347–371 | MR

[20] Gadylshin R. R., “Asimptotika sobstvennogo znacheniya singulyarno vozmuschennoi samosopryazhennoi ellipticheskoi zadachi s malym parametrom v granichnykh usloviyakh”, Differents. ur., 22:4 (1986), 640–652 | MR

[21] Kolton D., Kress R., Metody integralnykh uravnenii v teorii rasseyaniya, Mir, M., 1987 | MR

[22] Gotlib V. Yu., “Rasseyanie na kruglom rezonatore s uzkoi schelyu kak zadacha teorii vozmuschenii”, DAN SSSR, 287:5 (1986), 1109–1113 | MR