On the connection between spectral and oscillation properties of the Sturm–Liouville matrix problem
Sbornik. Mathematics, Tome 31 (1977) no. 3, pp. 365-378 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@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  - 
%0 Journal Article
%A F. S. Rofe-Beketov
%A A. M. Khol'kin
%T On the connection between spectral and oscillation properties of the Sturm–Liouville matrix problem
%J Sbornik. Mathematics
%D 1977
%P 365-378
%V 31
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1977_31_3_a4/
%G en
%F SM_1977_31_3_a4
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