Geodesic
The theory of extentions and zero-radius potentials with internal structure
Sbornik. Mathematics, Tome 65 (1990) no. 1, pp. 147-184 Cet article a éte moissonné depuis la source Math-Net.Ru

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A detailed spectral analysis is carried out for the Schrödinger operator with zero-radius potentials endowed with internal structure. Explicit expressions are obtained for the resolvents and spectral projections in the case when the internal operators are compact. The corresponding scattering problem is solved. Bibliography: 22 titles. 
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B. S. Pavlov; A. A. Shushkov. The theory of extentions and zero-radius potentials with internal structure. Sbornik. Mathematics, Tome 65 (1990) no. 1, pp. 147-184. http://geodesic.mathdoc.fr/item/SM_1990_65_1_a8/

[1] Berezin F. A., Faddeev L. D., “Zamechanie ob uravnenii Shredingera s singulyarnym potentsialom”, DAN SSSR, 137:5 (1961), 1011–1014 | MR | Zbl

[2] Birman M. Sh., “Usloviya suschestvovaniya volnovykh operatorov”, DAN SSSR, 143 (1962), 506–509 | MR | Zbl

[3] Birman M. Sh., Entina S. B., “Statsionarnyi podkhod v abstraktnoi teorii rasseyaniya”, Izv. AN SSSR. Ser. matem., 31 (1967), 401–430 | MR | Zbl

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

[5] Demkov Yu. P., Ostrovskii V. N., Metod potentsialov nulevogo radiusa v atomnoi fizike, Izd-vo LGU, L., 1975

[6] Kuperin Yu. A., Makarov K. A., Pavlov B. S., “Model rezonansnogo rasseyaniya sostavnykh chastits”, Teoret. i mat. fizika, 69:1 (1986), 100–114 | MR

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

[8] Minlos R. A., Faddeev L. D., “O tochechnom vzaimodeistvii dlya sistemy iz trekh chastits v kvantovoi mekhanike”, DAN SSSR, 141:6 (1961), 1335–1338 | MR

[9] Pavlov B. S., “Model potentsiala nulevogo radiusa s vnutrennei strukturoi”, Teoret. i mat. fizika, 59:3 (1984), 345–353 | MR

[10] Pavlov B. S, Popov I. Yu., “Model difraktsii na beskonechno uzkoi scheli i teoriya rasshirenii”, Vestn. LGU, 1983, no. 19, 36–43 | MR

[11] Pavlov B. S, Faddeev M. D., “Model svobodnykh elektronov i zadacha rasseyaniya”, Teoret. i mat. fizika, 55:2 (1983), 257–268 | MR

[12] Pavlov B. S, Faddeev M. D., “O rasseyanii na polom rezonatore s malym otverstiem”, 3ap. nauch. seminarov LOMI, 126 (1983), 159–169 | MR | Zbl

[13] Pavlov B. S, Shushkov A. A., “Potentsialy nulevogo radiusa i teoriya rasshirenii”, XI Vsesoyuzn. shkola po teorii operatorov v funktsionalnykh prostranstvakh. (tez. dokl. Ch. II), Chelyabinsk, 1986, 98

[14] Povzner A. Ya., “O razlozhenii proizvolnykh funktsii po sobstvennym funktsiyam operatora – $\Delta u\times cu$”, Matem. sb., 32(74) (1953), 109–156 | MR | Zbl

[15] Shirokov Yu. M., “Predstavlenie svobodnykh reshenii dlya uravneniya Shredingera s silno singulyarnymi sosredotochennymi potentsialami”, Teoret. i mat. fizika, 46:3 (1981), 291–299 | MR | Zbl

[16] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. T. 3. Teoriya rasseyaniya, Mir, M., 1982 | MR

[17] Shushkov A. A., “Struktura rezonansov dlya uravneniya Shredingera s simmetrichnymi potentsialami nulevogo radiusa”, Vestn. LGU, 1985, no. 15, 112–113 | MR | Zbl

[18] Shushkov L. A., “Struktura rezonansov dlya simmetrichnykh rasseivatelei”, Teoret. i mat. fizika, 64:3 (1985), 442–449 | MR

[19] Albeverio S., Gesztesy F., Hoegh-Krohn R., Holden H., Solvable Models in Quantum Mechanics. Part I., Preprint Univ. Oslo, 1985 | MR

[20] Albeverio S., Gesztesy F., Hoegh-Krohn R., Holden H., Solvable Models in Quantum Mechanics. Part II., Preprint Univ. Oslo, 1985

[21] Ikebe T., “Eingenf unctions expansions associated with the Schrödinger operators and their applications to scattering theory”, Arch. Rat. Mech. Anal., 5 (1960), 1–34 | DOI | MR | Zbl

[22] Fermi E., “Sopra lo spostamento per pressione delle righe elevate delle serie spettrali”, Nuovo Cim., 11 (1934), 157–166 | DOI | Zbl