@article{SM_1977_31_3_a4,
author = {F. S. Rofe-Beketov and A. M. Khol'kin},
title = {On the connection between spectral and oscillation properties of the {Sturm{\textendash}Liouville} matrix problem},
journal = {Sbornik. Mathematics},
pages = {365--378},
year = {1977},
volume = {31},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1977_31_3_a4/}
}
TY - JOUR AU - F. S. Rofe-Beketov AU - A. M. Khol'kin TI - On the connection between spectral and oscillation properties of the Sturm–Liouville matrix problem JO - Sbornik. Mathematics PY - 1977 SP - 365 EP - 378 VL - 31 IS - 3 UR - http://geodesic.mathdoc.fr/item/SM_1977_31_3_a4/ LA - en ID - SM_1977_31_3_a4 ER -
F. S. Rofe-Beketov; A. M. Khol'kin. On the connection between spectral and oscillation properties of the Sturm–Liouville matrix problem. Sbornik. Mathematics, Tome 31 (1977) no. 3, pp. 365-378. http://geodesic.mathdoc.fr/item/SM_1977_31_3_a4/
[1] B. M. Levitan, I. S. Sargsyan, Vvedenie v spektralnuyu teoriyu, Nauka, M., 1970 | MR | Zbl
[2] N. Danford, Dzh. T. Shvarts, Lineinye operatory. Spektralnaya teoriya, Mir, M., 1966
[3] M. M. Postnikov, Variatsionnaya teoriya geodezicheskikh, Nauka, M., 1965 | MR
[4] M. M. Postnikov, Vvedenie v teoriyu Morsa, Nauka, M., 1971 | MR
[5] Dzh. Milnor, Teoriya Morsa, Mir, M., 1965 | MR
[6] D. Gromol, V. Klingenberg, V. Meier, Rimanova geometriya v tselom, Mir, M., 1971
[7] V. B. Lidskii, “Ostsillyatsionnye teoremy dlya kanonicheskoi sistemy differentsialnykh uravnenii”, DAN SSSR, 102:5 (1955), 877–880 | MR | Zbl
[8] V. A. Yakubovich, “Ostsillyatornye svoistva reshenii kanonicheskikh uravnenii”, Matem. sb., 56(98) (1962), 3–42
[9] F. Atkinson, Diskretnye i nepreryvnye granichnye zadachi, Mir, M., 1968 | MR | Zbl
[10] G. A. Bliss, I. J. Schoenberg, “On separation, comparison and oscillation theorems for self-adjoint systems of linear second order differential equations”, Amer. J. Math., 53 (1931), 781–800 | DOI | MR | Zbl
[11] F. S. Rofe-Beketov, “Razlozhenie po sobstvennym funktsiyam beskonechnykh sistem differentsialnykh uravnenii v nesamosopryazhennom i samosopryazhennom sluchayakh, I”, Matem. sb., 51(93) (1960), 293–342 | MR | Zbl
[12] F. S. Rofe-Beketov, “Samosopryazhennye rasshireniya differentsialnykh operatorov v prostranstve vektor-funktsii”, DAN SSSR, 184:5 (1969), 1034–1037 | MR | Zbl
[13] F. S. Rofe-Beketov, “O samosopryazhennykh rasshireniyakh differentsialnykh operatorov v prostranstve vektor-funktsii”, Teoriya funktsii, funkts. analiz i ikh prilozheniya, no. 8, Kharkov, 1969, 3–24 | MR | Zbl
[14] M. L. Gorbachuk, V. A. Mikhailets, “Poluogranichennye samosopryazhennye rasshireniya simmetricheskikh operatorov”, DAN SSSR, 226:4 (1976), 765–767 | MR | Zbl
[15] V. I. Gorbachuk, M. L. Gorbachuk, “Nekotorye voprosy spektralnoi teorii differentsialnykh uravnenii ellipticheskogo tipa v prostranstve vektor-funktsii na konechnom intervale”, Ukr. matem. zh., 28:1 (1976), 12–26 | MR | Zbl
[16] F. S. Rofe-Beketov, Kand. dissertatsiya, KhPI im. V. I. Lenina, Kharkov, 1961
[17] M. L. Gorbachuk, “O spektralnykh funktsiyakh differentsialnogo uravneniya vtorogo poryadka s operatornymi koeffitsientami”, Ukr. matem. zh., 18:2 (1966), 3–21 | MR | Zbl
[18] I. M. Glazman, Pryamye metody kachestvennogo spektralnogo analiza, Fizmatgiz, M., 1963 | MR
[19] M. A. Naimark, Lineinye differentsialnye operatory, Nauka, M., 1969 | MR
[20] N. I. Akhiezer, I. M. Glazman, Teoriya lineinykh operatorov v gilbertovom prostranstve, Nauka, M., 1966 | MR | Zbl
[21] L. I. Vainerman, M. L. Gorbachuk, “O samosopryazhennosti poluogranichennykh abstraktnykh differentsialnykh operatorov”, Ukr. matem. zh., 22:6 (1970), 806–808 | MR | Zbl
[22] A. G. Brusentsev, F. S. Rofe-Beketov, “Usloviya samosopryazhennosti silno ellipticheskikh sistem proizvolnogo poryadka”, Matem. sb., 95(137) (1974), 108–129 | MR | Zbl
[23] V. I. Khrabustovskii, “O vozmuschenii spektra samosopryazhennykh differentsialnykh operatorov proizvolnogo poryadka s periodicheskimi matrichnymi koeffitsientami”, Matem. fizika i funkts. analiz, Trudy FTINT AN USSR, 5, 1974, 123–140
[24] F. Khartman, Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR | Zbl
[25] M. G. Gasymov, V. V. Zhikov, B. M. Levitan, “Usloviya diskretnosti i konechnosti otritsatelnogo spektra operatornogo uravneniya Shredingera”, Matem. zametki, 2:5 (1967), 531–538 | MR | Zbl
[26] D. R. Yafaev, “Ob otritsatelnom spektre operatornogo uravneniya Shredingera”, Matem. zametki, 7:6 (1970), 753–763 | Zbl