Aleksandrov and Kolmogorov in Dnepropetrovsk
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 38 (1983) no. 4, pp. 41-55 Cet article a éte moissonné depuis la source Math-Net.Ru

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S. M. Nikol'skii. Aleksandrov and Kolmogorov in Dnepropetrovsk. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 38 (1983) no. 4, pp. 41-55. http://geodesic.mathdoc.fr/item/RM_1983_38_4_a4/

[1] P. S. Alexandroff, “Sur l'invariance topologique des ensembles complémentaires aux ensembles (A)”, Matem. sb., 31:2 (1923), 310–318 | Zbl

[2] P. S. Alexandroff, “Sur les ensembles complémentaires aux ensembles (A)”, Fund. Math., 5 (1924), 100–105

[3] A. N. Kolmogoroff, “Sur une série de Fourier–Lebesque divergente partout”, C. R. Acad. Sci., 183 (1926), 1327–1329

[4] A. N. Kolmogoroff, “Zur Grössenoranuhg des restgliedes Fourierschen Reihen differenzierbares Funktionen”, Ann. of Math., 36 (1935), 521–526 | DOI | MR

[5] A. N. Kolmogoroff, “Über die beste Annaherung von Funktionen eines gegebenen Funktionen classe”, Ann. of Math., 37 (1930), 107–110 | DOI | MR

[6] A. H. Kolmogorov, “O neravenstve mezhdu verkhnimi granyami posledovatelnykh proizvodnykh proizvolnoi funktsii na beskonechnom intervale”, Uchenye zap. un-ta, 30, M., 1939, 3–16

[7] B. C. Vladimirov, I. I. Markush, Vladimir Andreevich Steklov – uchenyi i organizator nauki, Nauka, M., 1981 | MR

[8] V. M. Alekseev, E. M. Galeev, V. M. Tikhomirov, Sbornik zadach po optimizatsii, Nauka, M., 1983 | MR

[9] N. I. Akhiezer, M. G. Krein, “O nailuchshem priblizhenii trigonometricheskimi summami differentsiruemykh periodicheskikh funktsii”, DAN, 15 (1937), 107–112

[10] O. V. Besov, V. P. Ilin, S. M. Nikolskii, Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | MR | Zbl

[11] A. S. Bezlyudnyi, “Priblizhenie periodicheskikh funktsii dvukh peremennykh interpolyatsionnymi trigonometricheskimi polinomami”, DAN, 65 (1949), 257–260 | MR

[12] S. V. Bochkarëv, “Metod usrednenii v teorii ortogonalnykh ryadov i nekotorye voprosy teorii bazisov”, Trudy Matem. in-ta im. V. A. Steklova, 146, 1978, 1–86 | MR

[13] O. V. Besov, V. P. Ilin, S. M. Nikolskii, Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | MR | Zbl

[14] P. T. Bugaets, “Asimptoticheskaya otsenka ostatka pri priblizhenii funktsii dvukh peremennykh summami Fure”, DAN, 79 (1951), 557–560 | Zbl

[15] A. P. Buslaev, G. G. Magaril-Ilyaev, V. M. Tikhomirov, “O suschestvovanii ekstremalnykh funktsii v neravenstvakh dlya proizvodnykh”, Matem. zametki, 32:6 (1982), 823–834 | MR | Zbl

[16] L. L. Verbitskii, “Ob odnom sposobe summirovaniya interpolyatsionnykh polinomov”, Nauchn. zap. un-ta, 21, Dnepropetrovsk, 1940, 113–119

[17] Din Zing, V. M. Tikhomirov, “O neravenstvakh dlya proizvodnykh v metrike $L_2$”, Vestn. MGU, ser. matem., mekh., 1978, no. 2, 7–11

[18] A. Ya. Volpert, “O gomeomorfizme schetnykh mnozhestv”, Matem. sb., 29(71) (1951), 677–698 | MR | Zbl

[19] V. K. Dzyadyk, “O nailuchshem priblizhenii na klasse periodicheskikh funktsii, imeyuschikh ogranichennuyu $s$-yu proizvodnuyu”, Izv. AN, ser. matem., 17 (1953), 135–162 | MR

[20] V. K. Dzyadyk, V. A. Dubovin, “K neravenstvam A. N. Kolmogorova o zavisimosti mezhdu verkhnimi granyami proizvodnykh veschestvennykh funktsii dannykh na vsei osi”, UMZh, 27:3 (1975), 291–299 | MR

[21] G. Ya. Doronin, “Nekotorye neravenstva dlya priblizhenii trigonometricheskimi polinomami”, DAN, 69 (1948), 487–490 | MR

[22] R. S. Ismagilov, “Poperechniki mnozhestv v lineinykh normirovannykh prostranstvakh i priblizhenie funktsii trigonometricheskimi mnogochlenami”, UMN, 29:3 (1974), 161–178 | MR | Zbl

[23] V. N. Konovalov, “Tochnye neravenstva dlya norm funktsii, tretikh chastnykh, vtorykh smeshannykh ili kosykh proizvodnykh”, Matem. zametki, 23:1 (1978), 67–78 | MR | Zbl

[24] B. S. Kashin, “Poperechniki nekotorykh konechnomernykh mnozhestv i klassov gladkikh funktsii”, Izv. AN, ser. matem., 41:2 (1977), 334–351 | MR | Zbl

[25] N. P. Korneichuk, “Tochnaya konstanta v teoreme D. Dzheksona o nailuchshem ravnomernom priblizhenii nepreryvnykh periodicheskikh funktsii”, DAN, 145:3 (1962), 514–515

[26] V. T. Kondurar, “Sur Pintegrate de Stiltjes”, Matem. sb., 2(44) (1937), 361–366 | Zbl

[27] S. M. Nikolskii, “Priblizhenie periodicheskikh funktsii trigonometricheskimi mnogochlenami”, Trudy Matem. in-ta im. V. A. Steklova, 15, 1945, 1–76 | MR | Zbl

[28] S. M. Nikolskii, “O nailuchshem priblizhenii mnogochlenami funktsii, udovletvoryayuschikh usloviyu Lipshitsa”, Izv. AN, ser. matem., 10:4 (1946), 295–322 | MR | Zbl

[29] S. M. Nikolskii, Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR

[30] S. M. Nikolskii, “Otryvki iz vospominanii o A. I. Maltseve”, UMN, 27:4 (1972), 223–230 | MR

[31] K. I. Oskolkov, “Otsenka priblizheniya nepreryvnykh funktsii podposledovatelnostyami summ Fure”, Trudy Matem. in-ta im. V. A. Steklova, 134 (1975), 240–253 | MR | Zbl

[32] V. T. Pinkevich, “O poryadke ostatochnogo chlena ryada Fure funktsii, differentsiruemykh v smysle Weyl'ya”, Izv. AN, 4 (1940), 521–528 | Zbl

[33] A. Rodov, “Zavisimosti mezhdu verkhnimi granyami proizvodnykh funktsii deistvitelnogo peremennogo”, Izv. AN, ser. matem., 10 (1946), 257–270 | MR | Zbl

[34] S. L. Sobolev, Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, LGU, 1950; РќРѕРІРѕСЃРёР±РёСЂСЃРє, 1962

[35] S. B. Stechkin, “O nailuchshem priblizhenii zadannykh klassov funktsii lyubymi polinomami”, UMN, 9:1 (1954), 133–134 | Zbl

[36] S. B. Stechkin, “Nailuchshee priblizhenie lineinykh operatorov”, Matem. zametki, 1:2 (1967), 137–148 | Zbl

[37] A. F. Timan, “Ob odnom metode priblizheniya nepreryvnykh funktsii trigonometricheskimi polinomami”, Izv. AN, ser. matem., 11 (1947), 263–282 | MR | Zbl

[38] V. M. Tikhomirov, “Poperechniki mnozhestv v funktsionalnykh prostranstvakh i teoriya priblizhenii”, UMN, 15:3 (1960), 81–120 | MR | Zbl

[39] A. D. Scherbina, “Ob odnom metode summirovaniya ryadov, sopryazhennykh s ryadami Fure”, Nauchn. zap. un-ta, 25, Dnepropetrovsk, 1941, 45–61

[40] I. M. Ganzburg, “Ob odnom metode priblizheniya nepreryvnykh funktsii trigonometricheskimi summami”, DAN, 64 (1949), 13–16 | MR | Zbl

[41] E. Gagliardo, “Caraterizationi delle trace sulla frontiers relative ad alcune classi di funzioni in variabili”, Rend. Semin, matem. un-ta di Padova, 27 (1957), 284–305 | MR | Zbl

[42] L. Carleson, “On convergence and growth of partial sums of Fourier series”, Acta Math., 116 (1966), 135–155 | DOI | MR

[43] I. J. Schoenberg, Cavaretta, “Solution of Landau's problem concerning high derivatives on the halfline”, Konstruktivnaya teoriya funktsii (Varna, 1970), Trudy matem. konferentsii, 1972, 297–308 | MR | Zbl

[44] E. M. Stein, “Functions of exponential type”, Ann. of Math., 65:4 (1957), 582–592 | DOI | MR | Zbl

[45] A. P. Bulanov, V. M. Tikhomirov, “O neravenstvakh dlya proizvodnykh v mnogomernom sluchae”, Matem. zametki, 25:1 (1979), 59–73 | MR

[46] J. Favard, Matematisk Tidskrift (B), 1936, 81–94 | Zbl

[47] S. M. Nikolskii, “Ob interpolirovanii i nailuchshem priblizhenii differentsiruemykh periodicheskikh funktsii trigonometricheskimi polinomami”, Izv. AN, ser. matem., 10 (1946), 393–410

[48] V. N. Temlyakov, “Asimptoticheskoe povedenie nailuchshikh priblizhenii nepreryvnykh funktsii”, Izv. AN, ser. matem., 41:3 (1977), 587–606 | MR

[49] V. N. Temlyakov, “Priblizhenie funktsii s ogranichennoi smeshannoi raznostyu trigonometricheskimi polinomami i poperechniki nekotorykh klassov funktsii”, Izv. AN, ser. matem., 46:1 (1982), 171–186 | MR | Zbl

[50] S. A. Telyakovskii, “Priblizhenie differentsiruemykh funktsii chastnymi summami ikh ryadov Fure”, Matem. zametki, 4 (1968), 291–300 | Zbl

[51] R. A. Hunt, “On the convergence of Fourier series. Orthogonal expansion and their continuous analoges”, Proceedings conference (Edvardsville. Illinois, 1967), South Illinois University, 1968, 235–255 | MR | Zbl

[52] L. D. Kudryavtsev, “Pryamye i obratnye teoremy vlozheniya. Prilozheniya k resheniyu variatsionnymi metodami ellipticheskikh uravnenii”, Trudy Matem. in-ta im. V. A. Steklova, 55, 1959, 3–182 | MR | Zbl

[53] P. I. Lizorkin, “Kharakteristika granichnykh znachenii funktsii iz $L^r_p(E_n)$ na giperploskostyakh”, DAN, 150 (1963), 984–986 | MR | Zbl

[54] P. I. Lizorkin, “Obobschennoe liuvillevskoe differentsirovanie i funktsionalnye prostranstva $L^r_p(R_n)$. Teoremy vlozheniya”, Matem. sb., 60(102) (1963), 325–353 | MR | Zbl

[55] S. V. Uspenskii, “O teoremakh vlozheniya dlya vesovykh klassov”, Trudy Matem. in-ta im. V. A. Steklova, 60, 1961, 282–303 | MR | Zbl

[56] P. L. Ulyanov, “Vlozhenie nekotorykh klassov funktsii”, Izv. AN, ser. matem., 32 (1968), 644–686

[57] L. N. Slobodetskii, “Prostranstva S. L. Soboleva drobnogo poryadka i ikh prilozhenie k kraevym zadacham dlya differentsialnykh uravnenii v chastnykh proizvodnykh”, DAN, 118:2 (1958), 243–246 | Zbl

[58] N. E. Lushpai, “Nailuchshie kvadraturnye formuly na klassakh differentsiruemykh periodicheskikh funktsii”, Matem. zametki, 6:4 (1969), 475–481 | MR | Zbl

[59] A. A. Zhensykbaev, “Nailuchshaya kvadraturnaya formula dlya nekotorykh klassov periodicheskikh differentsiruemykh funktsii”, Izv. AN, ser., matem., 41:5 (1977), 1110–1124 | MR | Zbl

[60] A. A. Ligun, “Tochnye neravenstva dlya splain-funktsii i nailuchshie kvadraturnye formuly dlya nekotorykh klassov funktsii”, Matem. zametki, 19:6 (1976), 913–926 | MR | Zbl

[61] V. P. Motornyi, “O nailuchshei kvadraturnoi formule vida $\sum_{i=1}^np_if(x_i)$ dlya nekotorykh klassov periodicheskikh differentsiruemykh funktsii”, Izv. AN, ser. matem., 38:3 (1974), 583–614 | MR | Zbl

[62] V. F. Babenko, “Tochnaya asimptotika ostatkov optimalnykh dlya nekotorykh klassov funktsii vesovykh kubaturnykh formul”, Matem. zametki, 20:4 (1976), 589–595 | MR | Zbl

[63] V. L. Velikii, “Ermitovy splainy i svyazannye s nimi kvadraturnye formuly dlya nekotorykh klassov differentsiruemykh funktsii”, Izv. vuzov, matem., 1976, no. 5, 15–28

[64] N. P. Korneichuk, “O nailuchshem ravnomernom priblizhenii na nekotorykh klassakh nepreryvnykh funktsii”, DAN, 140:4 (1961), 748–751

[65] N. P. Korneichuk, “Ekstremalnye znacheniya funktsionalov i nailuchshee priblizhenie na klassakh periodicheskikh funktsii”, Izv. AN, ser. matem., 35 (1971), 93–124 | MR

[66] S. M. Nikolskii, “K voprosu ob otsenkakh priblizhenii kvadraturnymi formulami”, UMN, 5:2(36) (1950), 165–177 | MR

[67] S. M. Nikolskii, “Kvadraturnye formuly”, Izv. AN, ser. matem., 16 (1952), 181–196

[68] S. M. Nikolskii, Kvadraturnye formuly, Gostekhizdat, M., 1958 | MR

[69] N. P. Korneichuk, N. E. Lushpai, “Nailuchshie kvadraturnye formuly dlya klassov differentsiruemykh funktsii i kusochno-polinomialnoe priblizhenie”, Izv. AN, ser. matem., 33:6 (1969), 1416–1437