Extension theory and localization of resonances for domains of trap type
Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 209-234 Cet article a éte moissonné depuis la source Math-Net.Ru

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The existence of a series of resonances located near the real axis is proved for the problem of scattering on a domain with a small aperture (narrow slit) (a domain of trap type). A method is presented for computing the resonances, based on a model of slits of zero width, based in turn on the theory of selfadjoint extensions of symmetric operators.
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     author = {I. Yu. Popov},
     title = {Extension theory and localization of resonances for domains of trap type},
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     year = {1992},
     volume = {71},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1992_71_1_a12/}
}
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I. Yu. Popov. Extension theory and localization of resonances for domains of trap type. Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 209-234. http://geodesic.mathdoc.fr/item/SM_1992_71_1_a12/

[1] Laks P., Fillips R., Teoriya rasseyaniya, Mir, M., 1965

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

[3] Belorusets V. B., Fikhmanas R. F., “Raschet sobstvennoi chastoty i dobrotnosti rezonatora s malym otverstiem svyazi”, Tekhnika sredstv svyazi. Ser. «Radioizmeritelnaya tekhnika», 1976, no. 3, 8–12

[4] Pavlov B. S., “Teoriya rasshirenii i yavnoreshaemye modeli”, UMN, 42:6 (1987), 99–131 | MR

[5] Pavlov B. S, Faddeev M. D., “O rasseyanii na polnom rezonatore s malym otverstiem”, Zap. nauch. seminarov LOMI, 126, L., 1983, 159–169 | MR | Zbl

[6] Drozdov M. Yu., Popov I. Yu., “Schel nulevoi shiriny i trete kraevoe uslovie”, Vestn. LGU. Ser. 4, 3:18 (1987), 93–95

[7] Mikhlin S. G., Integralnye uravneniya i ikh prilozheniya, GITTL, M.–L., 1949

[8] Kellogg O. D., Foundations of potential theory, Springer, Berlin, 1929 | MR | Zbl

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

[10] Popov I. Yu., “Obosnovanie modeli schelei nulevoi shiriny dlya zadachi Dirikhle”, Sib. matem. zhurn., 30:2 (1989), 225–230

[11] Mazya V. G., Nazarov S. A., Plamenevskii B. A., “Asimptotika reshenii zadachi Dirikhle v oblasti s vyrezannoi tonkoi trubkoi”, Matem. sb., 116(158) (1981), 187–217 | MR

[12] Zimnev M. M, Popov I. Yu., “Vybor parametrov modeli schelei nulevoi shiriny”, ZhVM i MF, 27:3 (1987), 466–470 | MR | Zbl

[13] Khermander L., Lineinye differentsialnye operatory s chastnymi proizvodnymi, Mir, M., 1965 | MR

[14] Berkhin P. E., “K zadache difraktsii na tonkom ekrane”, Sib. matem. zhurn., 25:1 (1984), 39–52 | MR | Zbl

[15] Khruslov E. Ya., “O rezonansnykh yavleniyakh v odnoi zadache difraktsii”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozh., no. 6, izd-vo KhGU, Kharkov, 1968, 111–129

[16] Voitovich N. N., Katsenelenbaum B. Z., Sivov A. N., Obobschennyi metod sobstvennykh kolebanii v teorii difraktsii, Nauka, M., 1977 | MR | Zbl

[17] Gokhberg I. Ts., Sigal E. I., “Operatornoe obobschenie teoremy o logarifmicheskom vychete i teoremy Rushe”, Matem. sb., 84(126) (1971), 607–629 | Zbl

[18] Pavlov B. S., “Faktorizatsiya matritsy rasseyaniya i seriinaya struktura ee kornei”, Izv. AN SSSR. Ser. matem., 37:1 (1973), 217–246 | Zbl