Spectral properties of a class of boundary value problems
Sbornik. Mathematics, Tome 42 (1982) no. 3, pp. 387-398 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper studies the eigenvalues of a boundary value problem with a weight of variable sign and an oscillating Green's function. Bibliography: 18 titles.
@article{SM_1982_42_3_a5,
     author = {Yu. S. Barkovskii and V. I. Yudovich},
     title = {Spectral properties of a~class of boundary value problems},
     journal = {Sbornik. Mathematics},
     pages = {387--398},
     year = {1982},
     volume = {42},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_42_3_a5/}
}
TY  - JOUR
AU  - Yu. S. Barkovskii
AU  - V. I. Yudovich
TI  - Spectral properties of a class of boundary value problems
JO  - Sbornik. Mathematics
PY  - 1982
SP  - 387
EP  - 398
VL  - 42
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1982_42_3_a5/
LA  - en
ID  - SM_1982_42_3_a5
ER  - 
%0 Journal Article
%A Yu. S. Barkovskii
%A V. I. Yudovich
%T Spectral properties of a class of boundary value problems
%J Sbornik. Mathematics
%D 1982
%P 387-398
%V 42
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1982_42_3_a5/
%G en
%F SM_1982_42_3_a5
Yu. S. Barkovskii; V. I. Yudovich. Spectral properties of a class of boundary value problems. Sbornik. Mathematics, Tome 42 (1982) no. 3, pp. 387-398. http://geodesic.mathdoc.fr/item/SM_1982_42_3_a5/

[1] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969 | MR

[2] Gantmakher F. R., Krein M. G., Ostsillyatsionnye matritsy i yadra i malye kolebaniya mekhanicheskikh sistem, Gostekhizdat, M., L., 1950

[3] Gantmakher F. R., “O nesimmetrichnykh yadrakh Kelloga”, DAN SSSR, 1:1 (1936), 3–5 | Zbl

[4] Teoriya gidrodinamicheskoi ustoichivosti, IL, M., 1958

[5] Yudovich V. I., “Vtorichnye techeniya i neustoichivost zhidkosti mezhdu vraschayuschimisya tsilindrami”, PMM, 30:688–698 (1966)

[6] Kalafati P. D., “O funktsiyakh Grina obyknovennykh differentsialnykh uravnenii”, DAN SSSR, 26:6 (1940), 535–539

[7] Karlin S., “Total positivity, approximation by splines, and Green's function of differential operators”, J. Approxim. Theory, 4 (1971), 91 | DOI | MR | Zbl

[8] Kollatts L., Zadachi na sobstvennye znacheniya, Nauka, M., 1968

[9] Polia G., Sege G., Zadachi i teoremy iz analiza, T. II, Nauka, M., 1978

[10] Krein M. G., Finkelshtein G. M., “O vpolne neotritsatelnykh funktsiyakh Grina obyknovennykh differentsialnykh operatorov”, DAN SSSR, 24:3 (1939), 220–223 | MR | Zbl

[11] Guld S., Variatsionnye printsipy v zadachakh o sobstvennykh znacheniyakh, Mir, M., 1970 | MR

[12] Grommer J., “Ganze transzendente Funktionen mit lauter reelen Nullstellen”, B. 144, J. reine angew. Math., 1914

[13] Krein M. G., O integralnykh uravneniyakh, funktsii raspredeleniya kotorykh ne monotonny, Sb. pamyati akad. D. A. Grave, GONTI, M., L., 1940 | MR

[14] Levin A. Yu., Stepanov G. D., “Odnomernye kraevye zadachi s operatorami, ne ponizhayuschimi chisla peremen znaka. II”, Sib. matem. zh., 17:4 (1976), 813–830 | MR | Zbl

[15] Barkovskii Yu. S., Yudovich V. I., “Rozhdenie vikhrei Teilora v sluchae raznovraschayuschikhsya tsilindrov i spektralnye svoistva odnogo klassa kraevykh zadach”, DAN SSSR, 242:4 (1978), 784–787 | MR | Zbl

[16] Barkovskii Yu. S., Yudovich V. I., “Spektralnye svoistva konechnomernykh operatorov i problema momentov”, Izv. SKNTs VSh, ser. estestv. nauki, 1975, no. 4, 49–56 | MR

[17] Karlin S., Pinkus A., “Oscillation properties of generalized characteristic polynominals for totally positive and positive definite matrices”, Linear Algebra and Appl., 8:4 (1974), 281–312 | DOI | MR | Zbl

[18] Kurant R., Gilbert D., Metody matematicheskoi fiziki, t. 1, M., L., 1951