On separation conditions for the spectral components of a~dissipative operator
Izvestiya. Mathematics , Tome 9 (1975) no. 1, pp. 113-137.

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Conditions for separating the invariant subspaces corresponding to the absolutely continuous, discrete and singular spectrum of an abstract dissipative operator are obtained in terms of the characteristic function of the operator. The results are applied to ordinary differential operators with real potential and complex boundary conditions. Bibliography: 20 items.
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B. S. Pavlov. On separation conditions for the spectral components of a~dissipative operator. Izvestiya. Mathematics , Tome 9 (1975) no. 1, pp. 113-137. http://geodesic.mathdoc.fr/item/IM2_1975_9_1_a5/

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

[2] Pavlov B. S., “O nepreryvnom spektre rezonansov na nefizicheskom liste”, Dokl. AN SSSR, 206:2 (1972), 1301–1304 | MR | Zbl

[3] Nad B., Foiash Ch., Garmonicheskii analiz operatorov v gilbertovom prostranstve, Mir, M., 1970 | MR

[4] Adamyan V. M., Arov D. Z., “Ob unitarnykh stsepleniyakh poluunitarnykh operatorov”, Matematicheskie issledovaniya, tom 1, vyp. 1, Kishinev, 1966, 3–63

[5] Gofman K., Banakhovy prostranstva sistematicheskikh funktsii, IL, M., 1963

[6] Sakhnovich L. A., “Dissipativnye operatory s absolyutno nepreryvnym spektrom”, Tr. Mosk. matem. ob-va, 19, 1968, 213–270

[7] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M., L., 1950

[8] Lyantse V. E., “O differentsialnom operatore so spektralnymi osobennostyami”, Matem. sb., 64(103):4 (1964), 521–661

[9] Gasymov M. G., Maksudov F. G., “O glavnoi chasti rezolventy nesamosopryazhennykh operatorov v okrestnosti spektralnykh osobennostei”, Funktsionalnyi analiz, 6:3 (1972), 16–24 | MR | Zbl

[10] Fefferman C., Stein E., “Some maximal inequalities”, Amer. J. Math., 93:1 (1971), 107–115 | DOI | MR | Zbl

[11] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov, Nauka, M., 1965

[12] Nikolskii N. K., Pavlov B. S., “Bazisy iz sobstvennykh vektorov vpolne neunitarnykh szhatii i kharakteristicheskaya funktsiya”, Izv. AN SSSR. Ser. matem., 34 (1970), 90–133 | MR

[13] Titchmarsh E., Razlozheniya po sobstvennym funktsiyam, svyazannye s differentsialnymi uravneniyami vtorogo poryadka, t. I, II, IL, M., 1960

[14] Faddeev L. D., “Obratnaya zadacha kvantovoi teorii rasseyaniya”, Uspekhi matem. nauk, XIV:4(88) (1959), 57–119 | MR

[15] Naimark M. A., “Issledovanie spektra i razlozhenie po sobstvennym funktsiyam nesamosopryazhennogo differentsialnogo operatora vtorogo poryadka na poluosi”, Tr. Mosk. matem. ob-va, 3, 1954, 181–270 | MR | Zbl

[16] Pavlov B. S., “O nesamosopryazhennom operatore Shredingera”, Problemy matematicheskoi fiziki, no. 1, LGU, 1966, 102–132

[17] Pavlov B. S., “O nesamosopryazhennom operatore Shredingera, II”, Problemy matematicheskoi fiziki, no. 2, LGU, 1967, 133–157

[18] Pavlov B. S., “O nesamosopryazhennom operatore Shredingera, III”, Problemy matematicheskoi fiziki, no. 3, LGU, 1968, 59–80

[19] Warschawski S., “On differentiability at the boundary in conformal mapping”, Proc. Amer. Math. Soc., 12:4 (1961), 614–620 | DOI | MR | Zbl

[20] V. E. Katsnelson, “Ob usloviyakh bazisnoi sistemy kornevykh vektorov nekotorykh klassov operatorov”, Funktsionalnyi analiz i ego prilozheniya, 1:2 (1967), 39–51 | MR