Mots-clés : nikol'skii-besov class
@article{TIMM_2015_21_4_a0,
author = {G. A. Akishev},
title = {Estimates for {Kolmogorov} widths of the {Nikol'skii} {\textemdash} {Besov} {\textemdash} {Amanov} classes in the {Lorentz} space},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {3--13},
year = {2015},
volume = {21},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a0/}
}
TY - JOUR AU - G. A. Akishev TI - Estimates for Kolmogorov widths of the Nikol'skii — Besov — Amanov classes in the Lorentz space JO - Trudy Instituta matematiki i mehaniki PY - 2015 SP - 3 EP - 13 VL - 21 IS - 4 UR - http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a0/ LA - ru ID - TIMM_2015_21_4_a0 ER -
G. A. Akishev. Estimates for Kolmogorov widths of the Nikol'skii — Besov — Amanov classes in the Lorentz space. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 3-13. http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a0/
[1] Krein S.G., Petunin Yu.I., Semenov E.M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978, 400 pp. | MR
[2] Kolyada V.I., “Vlozheniya drobnykh prostranstv Soboleva i otsenki preobrazovanii Fure”, Mat. sb., 192:7 (2001), 51–72 | DOI | MR | Zbl
[3] Blozinski A.P., “Multivariate rearragements and Banach function spaces with mixed norms”, Trans. Amer. Math. Soc., 263:1 (1981), 149–167 | DOI | MR | Zbl
[4] Nikolskii S.M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977, 456 pp. | MR
[5] Nikolskii S.M., “Funktsii s dominiruyuschei smeshannoi proizvodnoi, udovletvoryayuschei kratnomu usloviyu Geldera”, Sib. mat. zhurn., 4:6 (1963), 1342–1364
[6] Amanov T.I., “Teoremy predstavleniya i vlozheniya dlya funktsionalnykh prostranstv $SB$”, Tr. MIAN, 77 (1965), 5–34 | MR | Zbl
[7] Amanov T.I., Prostranstva differentsiruemykh funktsii s dominiruyuschei smeshannoi proizvodnoi, Nauka, Alma-Ata, 1976, 224 pp. | MR
[8] Lizorkin P.I., Nikolskii S.M., “Prostranstva funktsii smeshannoi gladkosti s dekompozitsionnoi tochki zreniya”, Tr. MIAN, 187 (1989), 143–161 | MR
[9] Kolmogoroff A., “Uber die beste Annaherung von funktionen einer gegeben Funktionenklasse”, Ann. Math., 37 (1936), 107–111 | DOI | MR
[10] Rudin W., “$L_{2}$-approximation by partial sums of orthogonal developments”, Duke Math. J., 19 (1952), 1–4 | DOI | MR | Zbl
[11] Stechkin S.B., “O nailuchshikh priblizheniyakh zadannykh klassov funktsii lyubymi polinomami”, Uspekhi mat. nauk, 9:1 (1954), 133–134 | Zbl
[12] Tikhomirov V.M., “Poperechniki mnozhestv v funktsionalnom prostranstve i teoriya nailuchshikh priblizhenii”, Uspekhi mat. nauk, 15:3 (1960), 81–120 | MR | Zbl
[13] Babadzhanov S.B., Tikhomirov V.M., “O poperechnikakh odnogo klassa v prostranstve $L^{p}$”, Izv. AN Uzb. SSR. Ser. fiziko-matematicheskaya, 1967, no. 2, 24–30 | Zbl
[14] Subbotin Yu.N., “Poperechnik klassa $W^{r}L$ v $L(0, 2\pi)$ i priblizhenie splain funktsiyami”, Mat. zametki, 7:1 (1970), 43–52 | MR
[15] Subbotin Yu.N., “Priblizhenie splain-funktsiyami i otsenki ee poperechnikov”, Tr. MIAN, 109 (1971), 35–60 | MR | Zbl
[16] Ismagilov R.S., “Ob $n$-mernykh poperechnikakh kompaktov v gilbertovom prostranstve”, Funktsion. analiz i ego prilozheniya, 2:2 (1968), 32–39 | MR | Zbl
[17] Ismagilov R.S., “Poperechniki mnozhestv v lineinykh normirovannykh prostranstvakh i priblizhenie funktsii trigonometricheskimi mnogochlenami”, Uspekhi mat. nauk, 29:3 (1974), 161–173 | MR
[18] Gluskin E.D., “Ob odnoi zadache o poperechnikakh”, Dokl. AN SSSR, 219:3 (1974), 527–530 | MR | Zbl
[19] Kashin B.S., “Poperechniki nekotorykh konechnomernykh mnozhestv i klassov gladkikh funkii”, Izv. AN SSSR. Cer. matematicheskaya, 41:2 (1977), 334–351 | MR
[20] Makovoz Y., “On trigonometric $n$-widths and their generalization”, J. Approx. Theory, 41:4 (1984), 361–366 | DOI | MR | Zbl
[21] Kashin B.S., “O poperechnikakh klassov Soboleva maloi gladkosti”, Vestn. MGU. Ser. matematika, mekhanika, 1981, no. 5, 50–54 | MR | Zbl
[22] Kulanin E.D., “Otsenki poperechnikov klassov Soboleva maloi gladkosti”, Vestn. MGU. Ser. matematika, mekhanika, 1983, no. 2, 24–30 | MR | Zbl
[23] Babenko K.I., “O priblizhenii odnogo klassa periodicheskikh funktsii mnogikh peremennykh trigonometricheskimi mnogochlenami”, Dokl. AN SSSR, 132:5 (1960), 982–985 | MR | Zbl
[24] Mityagin B.S., “Priblizhenie funktsii v prostranstvakh $L^{p}$ i $C$ na tore”, Mat. sb., 58:4 (1962), 397–414 | Zbl
[25] Telyakovskii S.A., “Nekotorye otsenki dlya trigonometricheskikh ryadov s kvazivypuklymi koeffitsientami”, Mat. sb., 63:3 (1964), 426–444
[26] Bugrov Ya.S., “Priblizhenie klassov funktsii s dominiruyuschei smeshannoi proizvodnoi”, Mat. sb., 64:3 (1964), 410–418 | MR | Zbl
[27] Galeev E.M., “Poperechniki po Kolmogorovu klassov periodicheskikh funktsii mnogikh peremennykh $W_{p}^{\bar{r}}$ i $H_{p}^{\bar{r}}$ v prostranstve $L_{q}$”, Izv. AN SSSR. Cer. matematicheskaya, 49:3 (1985), 916–934 | MR | Zbl
[28] Galeev E.M., “Poperechniki po Kolmogorovu klassov periodicheskikh funktsii odnoi i neskolkikh peremennykh”, Izv. AN SSSR. Cer. matematicheskaya, 54:2 (1990), 418–430 | MR
[29] Galeev E.M., “Poperechniki klassov Besova $B_{p, \theta}^{r}(\mathbb{T}^{d})$”, Mat. zametki, 69:5 (2001), 656–665 | DOI | MR | Zbl
[30] Temlyakov V.N., “Priblizhenie funktsii s ogranichennoi smeshannoi proizvodnoi”, Tr. MIAN, 178 (1986), 1–112 | MR | Zbl
[31] Temlyakov V.N., “Otsenki asimptoticheskikh kharakteristik klassov funktsii s ogranichennoi smeshannoi proizvodnoi ili raznostyu”, Tr. MIAN, 189 (1989), 138–168 | MR
[32] Din Zung, “Priblizhenie funktsii mnogikh peremennykh na tore trigonometricheskimi polinomami”, Mat. sb., 131:2 (1986), 251–271
[33] Belinskii E.S., “Priblizhenie “plavayuschei” sistemoi eksponent na klassakh periodicheskikh funktsii s ogranichennoi smeshannoi proizvodnoi”, Issledovaniya po teorii funktsii mnogikh veschestv. peremennykh, Yaroslavl, 1988, 16–33 | MR
[34] Belinskii E.S., “Otsenki dlya kolmogorovskikh poperechnikov klassov funktsii s usloviyami na smeshannuyu raznost v ravnomernoi metrike”, Mat. zametki, 50:5 (1991), 147–149 | MR
[35] Romanyuk A.S., “O nailuchshikh trigonometricheskikh priblizheniyakh i kolmogorovskikh poperechnikakh klassov Besova funktsii mnogikh peremennykh”, Ukr. mat. zhurn., 45:5 (1993), 663–675 | MR | Zbl
[36] Romanyuk A.S., “Kolmogorovskie poperechniki klassov Besova $B_{p,\theta}^{r}$ v metrike $L_{\infty}$”, Ukr. mat. vestnik, 2005, no. 2, 201–218 | MR | Zbl
[37] Romanyuk A.S., “Kolmogorovskie i trigonometricheskie poperechniki klassov Besova $B_{p, \theta}^{r}$ periodicheskikh funktsii mnogikh peremennykh”, Mat. sb., 197:1 (2006), 71–96 | DOI | MR | Zbl
[38] Heping Wang, Yongsheng Sun, “Kolmogorov widths between the anisotropic space and the space of functions with mixed smoothness”, J. Approx. Theory, 126:1 (2004), 52–59 | DOI | MR | Zbl
[39] Bazarkhanov D.B., “Otsenki nekotorykh approksimativnykh kharakteristik prostranstv Nikolskogo-Besova obobschennoi smeshannoi gladkosti”, Dokl. RAN, 426:1 (2009), 11–14 | MR | Zbl
[40] Akishev G., “On approximation of function classes in Lorentz spaces with anisotropic norm”, Anal. Theory Appl., 29:4 (2013), 358–372 | MR | Zbl
[41] Akishev G., “Neravenstva raznykh metrik dlya trigonometricheskikh polinomov”, Materialy nauchn.-prakt. konf. “Ualikhanovskie chteniya -9”, Kokshetau, 2004, 3–6
[42] Nursultanov E.D., “Neravenstva raznykh metrik S.M. Nikolskogo i svoistva posledovatelnosti norm summ Fure funktsii iz prostranstva Lorentsa”, Tr. MIAN, 255 (2006), 1–18 | MR
[43] Kashin B.S., “O nekotorykh svoistvakh matrits ogranichennykh operatorov iz prostranstva $l_{2}^{n}$ v $l_{2}^{m}$”, Izv. AN Arm. SSR. Matematika, 15:5 (1980), 379–394 | MR | Zbl
[44] Gluskin E.D., “Normy sluchainykh matrits i poperechniki konechnomernykh mnozhestv”, Mat. sb., 120:2 (1983), 180–189 | MR | Zbl