Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MZM_2021_110_1_a6, author = {R. A. Lasuriya}, title = {Inverse {Approximation} {Theorems} in the {Spaces} $S^{(p,q)}(\sigma^{m-1})$}, journal = {Matemati\v{c}eskie zametki}, pages = {75--89}, publisher = {mathdoc}, volume = {110}, number = {1}, year = {2021}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a6/} }
R. A. Lasuriya. Inverse Approximation Theorems in the Spaces $S^{(p,q)}(\sigma^{m-1})$. Matematičeskie zametki, Tome 110 (2021) no. 1, pp. 75-89. http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a6/
[1] R. A. Lasuriya, “Pryamye i obratnye teoremy priblizheniya funktsii, zadannykh na sfere v prostranstve $S^{(p,q)}(\sigma^m)$”, Ukr. matem. zhurn., 59:7 (2007), 901–911 | MR
[2] R. A. Lasuriya, “Pryamye i obratnye teoremy priblizheniya funktsii summami Fure–Laplasa v prostranstvakh $S^{(p,q)}(\sigma^{m-1})$”, Matem. zametki, 98:4 (2015), 530–543 | DOI
[3] R. A. Lasuriya, “Neravenstva tipa Dzheksona v prostranstvakh $S^{(p,q)}(\sigma^{m-1})$”, Matem. zametki, 105:5 (2019), 724–739 | DOI | MR
[4] R. A. Lasuriya, “Priblizheniya funktsii na sfere lineinymi metodami”, Ukr. matem. zhurn., 66:11 (2015), 1498–1511 | MR
[5] A. I. Stepanets, Metody teorii priblizhenii, Ch. 1, Pratsi In-tu matematiki NAN Ukraïni. Matematika ta iïzastosuvannya, 40, In-t matematiki NAN Ukraïni, Kiïv, 2002 | MR
[6] R. A. Lasuriya, “Approksimatsionnye kharakteristiki prostranstv $S^{(p,q)}(\sigma^m)$ funktsii, zadannykh na sfere”, Pratsi In-tu matematiki NAN Ukraïni. Ekstremalni zadachi teorii funktsii ta sumizhni pitannya, 46, In-t matematiki NAN Ukraïni, Kiïv, 2003, 89–115 | MR
[7] I. M. Stein, Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR | Zbl
[8] H. Berens, P.Ł. Butzer, S. Pawelke, “Limiterungsverfahren von Reihen medrdimensionver Kugelfunktionen und deren Saturationsverhalten”, Publ. Res. Inst. Math.Sci. A., 4:2 (1968), 201–268 | DOI | MR
[9] I. Stein, G. Veis, Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974 | Zbl
[10] N. Ya. Vilenkin, Spetsialnye funktsii i teoriya predstavlenii grupp, Nauka, M., 1965 | MR
[11] R. Askey, S. Wainger, “On the behavior of special classes of ultrasherical expansions. I”, J. Anal. Math., 15 (1965), 193–220 | DOI | MR
[12] V. F. Babenko, V. G. Doronin, A. A. Ligun, A. A. Shumeiko, “O neravenstvakh tipa Dzheksona dlya funktsii, zadannykh na sfere”, Ukr. matem. zhurn., 57:3 (2005), 291–304 | MR
[13] S. B Stechkin, “O poryadke nailuchshikh priblizhenii nepreryvnykh funktsii”, Izv. AN SSSR. Ser. matem., 15:3 (1951), 219–242 | MR | Zbl
[14] A. F. Timan, Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatlit, M., 1960 | MR
[15] M. F. Timan, Approksimatsiya i svoistva periodicheskikh funktsii, Naukova dumka, K., 2009
[16] G. G. Kushnirenko, “O priblizhenii funktsii, zadannykh na edinichnoi sfere, konechnymi sfericheskimi summami”, Nauch. dokl. vysshei shkoly. Ser. fiz.-matem. nauk, 1958, no. 4, 47–53
[17] G. G. Kushnirenko, “Nekotorye voprosy priblizheniya nepreryvnykh funktsii na edinichnoi sfere konechnymi sfericheskimi summami”, Tr. Kharkovskogo. politekhn. in-ta. Ser. inzh.-fiz., 256:3 (1959), 3–22
[18] Ar. S. Dzhafarov, “O poryadke nailuchshikh priblizhenii nepreryvnykh na edinichnoi sfere funktsii posredstvom konechnykh sfericheskikh summ”, Issledovaniya po sovremennym problemam konstruktivnoi teorii funktsii, AN Az. SSR, Baku, 1965, 46–52
[19] Ar. S. Dzhafarov, “O sfericheskikh analogakh klassicheskikh teorem Dzh. Dzheksona i S. N. Bernshteina”, Dokl. AN SSSR, 203:2 (1972), 278–281 | MR | Zbl
[20] S. Pawelke, “Über die approximationserdnung bei Kugelfunktionen und algebraischen polgnomen”, Tohoku Math. J., 24:3 (1972), 473–486 | DOI | MR
[21] P. L. Butzer, H. Johnen, “Lipschitz spaces on compact manifolds”, J. Funct. Anal., 7:2 (1971), 242–266 | DOI | MR
[22] P. I. Lizorkin, S. M. Nikolskii, “Priblizhenie na sfere v $L_2$”, Dokl. AN SSSR, 271:5 (1983), 1059–1063 | MR | Zbl
[23] P. I. Lizorkin, S. M. Nikolskii, “Priblizhenie sfericheskimi funktsiyami”, Issledovaniya po teorii differentsiruemykh funktsii mnogikh peremennykh i ee prilozheniyam. Chast 11, Sbornik rabot, Tr. MIAN SSSR, 173, 1986, 181–189 | MR | Zbl
[24] S. M. Nikolskii, P. I. Lizorkin, “Approksimatsiya funktsii na sfere”, Izv. AN SSSR. Ser. matem., 51:3 (1987), 635–651 | MR | Zbl
[25] S. M. Nikolskii, P. I. Lizorkin, “Funktsionalnye prostranstva na sfere, svyazannye s teoriei priblizhenii”, Matem. zametki, 41:4 (1987), 509–516 | MR | Zbl
[26] S. M. Nikolskii, P. I. Lizorkin, “Novyi podkhod k teorii funktsionalnykh prostranstv $B^r_{p,\theta}$ na sfere”, Issledovaniya po teorii differentsiruemykh funktsii mnogikh peremennykh i ee prilozheniyam. Chast 12, Tr. MIAN SSSR, 181, Nauka, M., 1988, 213–221 | MR | Zbl
[27] Kh. P. Rustamov, “Ob obratnykh teoremakh $L_p$-nailuchshego priblizheniya na sfere $S^{n-1}$”, Izv. AN Az. SSR. Ser. fiz.-tekh. i matem. nauk, 1984, no. 6, 6–12
[28] Kh. P. Rustamov, “O pryamykh i obratnykh teoremakh nailuchshego $L_p$-priblizheniya na sfere”, Dokl. AN SSSR, 294:4 (1987), 788–791 | MR | Zbl