@article{SM_1992_71_2_a10,
author = {A. P. Buslaev and V. M. Tikhomirov},
title = {Spectra of nonlinear differential equations and widths of {Sobolev} classes},
journal = {Sbornik. Mathematics},
pages = {427--446},
year = {1992},
volume = {71},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1992_71_2_a10/}
}
A. P. Buslaev; V. M. Tikhomirov. Spectra of nonlinear differential equations and widths of Sobolev classes. Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 427-446. http://geodesic.mathdoc.fr/item/SM_1992_71_2_a10/
[1] Kolmogorov A. N., “O nailuchshem priblizhenii funktsii zadannogo funktsionalnogo klassa”, Izbrannye trudy, Matematika i mekhanika, Nauka, M., 1985, 186–189 | MR
[2] Tikhomirov V. M., “Poperechniki mnozhestv v funktsionalnykh prostranstvakh i teoriya nailuchshikh priblizhenii”, UMN, 15:3 (1960), 81–120 | MR | Zbl
[3] Tikhomirov V. M., Babadzhanov S. B., “O poperechnikakh odnogo funktsionalnogo klassa v prostranstve $L_p$, $1\leqslant p$”, Izv. AN UzSSR. Ser. fiz.-matem., 2 (1967), 24–30 | Zbl
[4] Makovoz Yu. I., Teoremy o nailuchshem priblizhenii i poperechnikakh mnozhestv v banakhovykh prostranstvakh, Dis. ... kand. fiz.-matem. nauk, Izd-vo BGU, Minsk, 1969
[5] Tikhomirov V. M., “Nekotorye voprosy teorii priblizhenii”, Matem. zametki, 9:5 (1971), 593–607
[6] Tikhomirov V. M., “Nailuchshie metody priblizheniya i interpolirovaniya differentsiruemykh funktsii v prostranstve $C[-1, 1]$”, Matem. sb., 80(122) (1969), 290–304 | Zbl
[7] Tikhomirov V. M., “Teoriya ekstremalnykh zadach i teoriya priblizhenii”, Banach Center Publications, 4 (1979), 273–285 | MR
[8] Micchelli Ch., Pinkus A., “On $n$-widths in $L^\infty$”, Trans. Amer. Math. Soc., 234:1 (1977), 139–174 | DOI | MR | Zbl
[9] Ligun A. A., “O poperechnikakh nekotorykh klassov periodicheskikh funktsii”, Matem. zametki, 27 (1980), 61–75 | MR | Zbl
[10] Makovoz Yu. I., “Poperechniki Sobolevskikh klassov i splainy, naimenee uklonyayuschiesya ot nulya”, Matem. zametki, 26:5 (1979), 805–812 | MR | Zbl
[11] Pinkus A., “On $n$-widths of periodic functions”, J. Anal. Math., 35 (1979), 209–235 | DOI | MR | Zbl
[12] Pinkus A., “$n$-widths of Sobolev spaces in $L_p$”, Constr. appr., 1985, no. 11, 15–62 | DOI | MR | Zbl
[13] Buslaev A. P., Tikhomirov V. M., “Nekotorye voprosy nelineinogo analiza i teorii priblizhenii”, DAN SSSR, 283:1 (1985), 13–18 | MR | Zbl
[14] Korneichuk N. P., Tochnye konstanty v teorii priblizheniya, Nauka, M., 1987 | MR
[15] Tikhomirov V. M., “A. N. Kolmogorov i teoriya priblizhenii”, UMN, 44:1 (1989), 83–122 | MR | Zbl
[16] Rayleigh J. W., “Some general theorems relating to vibrations”, Proc. Lond. Mat. Soc., 4 (1873), 357–368
[17] Weyl H., “Das asymptotische Verteilungsgesetz der Eigenlinearer partiellen Differentialgleichungen”, Math. Ann., 1912, 441–479 | DOI | MR | Zbl
[18] Kurant R., Gilbert D., Metody matematicheskoi fiziki. Izd. 2-e., t. I–II, GITTL, M.–L., 1951
[19] Landau L. D., Lifshits E. M., Mekhanika, GIFML, M., 1958
[20] Troitskii V. L., Petukhov L. V., Optimizatsiya formy uprugikh tel, Nauka, M., 1982 | MR
[21] Olkhoff N., Optimalnoe proektirovanie konstruktsii, Mir, M., 1981
[22] Andronov A. A., Vitt A. A., Khaikin S. E., Teoriya kolebanii, FM, M., 1959
[23] Lyusternik L. A., “Sur une classe d'equations différentielles nonlinéaires”, Matem. sb., 2 (1937), 1143–1168
[24] Lyusternik L. A., “Quelques remarques supplementaires sir les equations nonlineaires de type de Sturm - Liouville”, Matem. sb., 4 (1938), 227–232
[25] Krein M. G., “Ob uzlakh garmonicheskikh kolebanii mekhanicheskikh sistem nekotorogo spetsialnogo vida”, Matem. sb., 41 (1934), 339–348 | Zbl
[26] Gantmakher F. R., Krein M. G., Ostsillyatsionnye matritsy, yadra i malye kolebaniya mekhanicheskikh sistem, Gostekhizdat, M., 1950
[27] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977 | MR | Zbl
[28] Danford N., Shvarts Dzh., Lineinye operatory. Obschaya teoriya, IL, M., 1962
[29] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1989 | MR
[30] Khardi G. G., Littlvud D. E., Polia G., Neravenstva, IL, M., 1948
[31] Tikhomirov V. M., Nekotorye voprosy teorii priblizhenii, MGU, M., 1976 | MR
[32] Pinkus A., $n$-widths in Approximation Theory, Springer, N. Y., 1985 | MR
[33] Buslaev A. P., “O variatsionnom opisanii spektra vpolne polozhitelnykh matrits i ekstremalnykh zadachakh teorii priblizhenii”, Matem. zametki, 47:1 (1990), 39–46 | MR | Zbl
[34] Daugavet I. K., Vvedenie v teoriyu priblizheniya funktsii, Izd-vo Leningr. u-ta, M., 1977 | MR | Zbl
[35] Buslaev A. P., “Ekstremalnye zadachi teorii priblizhenii i nelineinye kolebaniya”, DAN SSSR, 305:6 (1989), 1289–1294 | MR | Zbl