@article{SM_1991_68_1_a11,
author = {Nguy\^en Thị Thi\^eu Hoa},
title = {Some extremal problems on classes of functions determined by linear differential operators},
journal = {Sbornik. Mathematics},
pages = {213--255},
year = {1991},
volume = {68},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1991_68_1_a11/}
}
Nguyên Thị Thiêu Hoa. Some extremal problems on classes of functions determined by linear differential operators. Sbornik. Mathematics, Tome 68 (1991) no. 1, pp. 213-255. http://geodesic.mathdoc.fr/item/SM_1991_68_1_a11/
[1] Nikolskii S. M., Kvadraturnye formuly, Nauka, M., 1988 | MR
[2] Tikhomirov V. M., Boyanov B. D., “O nekotorykh vypuklykh zadachakh teorii priblizhenii”, Serdika B'lgarsko matem. spisanie, 5 (1979), 83–96 | MR | Zbl
[3] Boyanov B. D., Optimalno v'zstnovyavanie na funktsii i funktsionali, Dis. ... dokt. matem. nauk, Sofiiskii un-t, Sofiya, 1980
[4] Korneichuk N. P., Tochnye konstanty v teorii priblizheniya, Nauka, M., 1987 | MR
[5] Oskolkov K. I., “Ob optimalnosti kvadraturnoi formuly s ravnostoyaschimi uzlami na klassakh periodicheskikh funktsii”, DAN SSSR, 249:1 (1979), 49–52 | MR
[6] Chakhkiev M. A., “Lineinye differentsialnye operatory s veschestvennym spektrom i optimalnye kvadraturnye formuly”, Izv. AN SSSR, 48 (1984), 1078–1108 | MR | Zbl
[7] Babenko V. F., Grankina T. A., “O nailuchshikh kvadraturnykh formulakh na klassakh svertok s $O(M\Delta)$-yadrami”, Issledovanie po sovremennym problemam summirovaniya i priblizheniya funktsii i ikh prilozheniyam, 1982, 6–13, DGU, Dnepropetrovsk
[8] Nguen Tkhi Tkheu Khoa, UMN, 39:2 (1984), 177–178 | MR
[9] Nguen Tkhi Tkheu Khoa, “Nailuchshie kvadraturnye formuly i metody vosstanovleniya funktsii, opredelyaemykh yadrami, ne uvelichivayuschimi ostsillyatsiyu”, Matem. sb., 130(172) (1986), 105–119 | MR | Zbl
[10] Nakonechnaya T. V., O vosstanovlenii na klassakh svertok, RZh MAT 5B100 DEP., 1985
[11] Krein M. G., “K teorii nailuchshego priblizheniya periodicheskikh funktsii”, DAN SSSR, 18:4–5 (1938), 245–251
[12] Pinkus A., $n$-width in approximation theory, Springer-Verlag, Berlin, 1985 | MR
[13] Shevaldin V. T., “$L$-splainy i poperechniki”, Matem. zametki, 33:5 (1983), 735–744 | MR | Zbl
[14] Volodina I. N., “Exact value of widths of certain class of solutions of linear differential equations”, Analysis Math., 11:1 (1985), 85–92 | DOI | MR | Zbl
[15] Novikov S. I., “Poperechniki odnogo klassa periodicheskikh funktsii, opredelyaemogo differentsialnym operatorom”, Matem. zametki, 42:2 (1987), 194–206 | MR
[16] Nguen Tkhi Tkheu Khoa, “Teorema Rollya dlya differentsialnykh operatorov i nekotorye ekstremalnye zadachi teorii priblizhenii”, DAN SSSR, 295:6 (1987), 1313–1318
[17] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976 | MR
[18] Schoenberg I. J., “On variation diminishing integral operators of the convolution type”, Proc. Nat. Acad. Sci. U. S. A., 34 (1984), 164–169 | DOI | MR
[19] Mairhuber J. C., Schoenberg I. J., Williamson R. E., “On variation diminishing transformations of the circle”, Rend. Circ. Mat. Palermo, 8 (1959), 241–270 | DOI | MR | Zbl
[20] Karlin S., Total positivity, Stanford Univ., Stanford, 1968 | MR
[21] Polia G., Segë G., Zadachi i teoremy iz analiza, t. 2, Nauka, M., 1978
[22] Krein M. G., Nudelman A. A., Problema momentov Markova i ekstremalnye zadachi, Nauka, M., 1973 | MR
[23] Dzyadyk V. K., Vvedenie v teoriyu ravnomernogo priblizheniya funktsii polinomami, Nauka, M., 1977 | MR | Zbl
[24] Akhiezer N. I., Lektsii po teorii approksimatsii, Nauka, M., 1967
[25] Ogiewetzki I. I., “Generalization of the inequality of P. Civin”, Acta Math. Acad. Sci. Hung., 9 (1958), 133–135 | DOI | MR
[26] Favard J., “Sur les meilleures procedes d'approximation de certains classes de functions par des polynomes trigonometriques”, Bul. Sci. Math., 61 (1937), 209–224 | Zbl
[27] Akhiezer H. I. Krein M. G., “O nailuchshem priblizhenii trigonometricheskimi summami differentsiruemykh periodicheskikh funktsii”, DAN SSSR, 15:3 (1937), 107–112
[28] Akhiezer N. I., “O nailuchshem priblizhenii odnogo klassa nepreryvnykh periodicheskikh funktsii”, DAN SSSR, 17:9 (1937), 451–453
[29] Tikhomirov V. M., Nekotorye voprosy teorii priblizhenii, Izd-vo MGU, M., 1976 | MR
[30] Nguen Tkhi Tkheu Khoa, “Ob odnoi ekstremalnoi zadache dlya klassov svertok, ne uvelichivayuschikh ostsillyatsiyu”, Vestn. MGU. Ser. 1. Matematika. Mekhanika, 1982, no. 5, 3–7 | MR
[31] Nguen Tkhi Tkheu Khoa, “Neravenstvo Kolmogorova dlya differentsialnykh operatorov”, Vestn. MGU. Ser. 1. Matematika. Mekhanika, 1987, no. 1, 17–21
[32] Stein E. M., “Functions of exponential type”, Ann. Math., 65:3 (1957), 582–592 | DOI | MR | Zbl
[33] Tikhomirov V. M., “Teoriya priblizhenii”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 14, VINITI, M., 1987, 103–260 | MR
[34] Motornyi V. P., “O nailuchshei kvadraturnoi formule vida $\sum_{i=1}^np_if(x_i)$ dlya nekotorykh klassov periodicheskikh differentsiruemykh funktsii”, Izv. AN SSSR. Ser. matem., 38 (1974), 583–614 | MR | Zbl
[35] Zhensykbaev A. A., “Monosplainy minimalnoi normy i nailuchshie kvadraturnye formuly”, UMN, 36:4 (1981), 107–159 | MR | Zbl
[36] Nguen Tkhi Tkheu Khoa, Nailuchshie kvadraturnye formuly i metody vosstanovleniya na klassakh funktsii, zadavaemykh svertkami, ne uvelichivayuschimi ostsillyatsiyu, Dis. ... kand. fiz.-matem. nauk, MGU, M., 1985
[37] Tikhomirov V. M., “Nailuchshie metody priblizheniya i interpolirovaniya differentsiruemykh funktsii v prostranstve $C[-1,1]$”, Matem. sb., 80(122) (1969), 290–304 | Zbl
[38] Favard J., “Sur e'interpolation”, J. Math. Pures Appl., 19 (1940), 281–306 | MR | Zbl
[39] Smolyak S. A., Ob odnom optimalnom vosstanovlenii funktsii i funktsionalov ot nikh, Dis. ... kand. fiz.-matem. nauk, MGU, M., 1965
[40] Shevaldin V. T., “Nekotorye zadachi ekstremalnoi interpolyatsii v srednem dlya lineinykh differentsialnykh operatorov”, Tr. MIAN, 164 (1983), 203–240 | MR | Zbl
[41] Vallee Poussin Ch. J., “Sur e'eqiiation differentielle du second ordre. Determination d'une integrate par deux valeurs assignees. Extension aux equations dorden”, J. Math. Pure et Appl., 8 (1929), 125–144 | Zbl