Keywords: uniform knots.
@article{TIMM_2015_21_4_a28,
author = {V. T. Shevaldin and O. Ya. Shevaldina},
title = {Upper bounds for uniform {Lebesgue} constants of interpolational periodic sourcewise representable splines},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {309--315},
year = {2015},
volume = {21},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a28/}
}
TY - JOUR AU - V. T. Shevaldin AU - O. Ya. Shevaldina TI - Upper bounds for uniform Lebesgue constants of interpolational periodic sourcewise representable splines JO - Trudy Instituta matematiki i mehaniki PY - 2015 SP - 309 EP - 315 VL - 21 IS - 4 UR - http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a28/ LA - ru ID - TIMM_2015_21_4_a28 ER -
%0 Journal Article %A V. T. Shevaldin %A O. Ya. Shevaldina %T Upper bounds for uniform Lebesgue constants of interpolational periodic sourcewise representable splines %J Trudy Instituta matematiki i mehaniki %D 2015 %P 309-315 %V 21 %N 4 %U http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a28/ %G ru %F TIMM_2015_21_4_a28
V. T. Shevaldin; O. Ya. Shevaldina. Upper bounds for uniform Lebesgue constants of interpolational periodic sourcewise representable splines. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 309-315. http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a28/
[1] Shevaldin V.T., Istokoobraznye splainy i poperechniki klassov periodicheskikh funktsii, dis.. d-ra fiz.-mat. nauk, In-t matematiki i mekhaniki UrO RAN, Ekaterinburg, 1996, 193 pp.
[2] Korneichuk N.P., Tochnye konstanty v teorii priblizheniya, Nauka, M., 1987, 424 pp. | MR
[3] Stepanets A.I., Metody teorii priblizhenii, v 2 ch., v. 1, 2, In-t matematiki NAN Ukrainy, Kiev, 2002, 427,468 pp.
[4] Shevaldin V.T., “Otsenki snizu poperechnikov klassov istokoobrazno predstavimykh funktsii”, Tr. MIAN, 189 (1989), 185–201 | MR
[5] Alberg Dzh., Nilson., Uolsh Dzh., Teoriya splainov i ee prilozheniya, Mir, M., 1972, 320 pp. | MR
[6] Subbotin Yu.N., “O svyazi mezhdu konechnymi raznostyami i sootvetstvuyuschimi proizvodnymi”, Tr. MIAN SSSR, 78 (1965), 24–42 | MR | Zbl
[7] Kushpel A.K., “Tochnye otsenki poperechnikov klassov svertok”, Izv. RAN. Ser. matematicheskaya, 52:6 (1988), 1305–1322 | MR
[8] Richards F., “Best bounds for the uniform periodic spline interpolation operator”, J. Approx. Theory, 7:3 (1973), 302–317 | DOI | MR | Zbl
[9] Zhensykbaev A.A., “Tochnye otsenki ravnomernogo priblizheniya nepreryvnykh funktsii splainami $r$-go poryadka”, Mat. zametki, 13:2 (1973), 217–228
[10] Subbotin Yu.N., Telyakovskii S.A., “Asimptotika konstant Lebega periodicheskikh interpolyatsionnykh splainov s ravnootstoyaschimi uzlami”, Mat. sb., 191:8 (2000), 131–140 | DOI | MR | Zbl
[11] Kim V.A., “Tochnye konstanty Lebega dlya interpolyatsionnykh $\mathcal L$-splainov formalno samosopryazhennogo differentsialnogo operatora”, Tr. In-ta matematiki i mekhaniki UrO RAN, 17:3 (2011), 169–177
[12] Stepanets A.I., Serdyuk A.S., “O suschestvovanii interpolyatsionnykh $SK$-splainov”, Ukr. mat. zhurn., 46:11 (1994), 1546–1553 | MR | Zbl
[13] Serdyuk A.S., Bodenchuk V.V., “Exact values of Kolmogorov widths of classes of Poisson integrals”, J. Approx. Theory, 173:1 (2013), 89–109 | DOI | MR | Zbl
[14] Pinkus A., “On $n$-widths of periodic functions”, J. Anal. Math., 35 (1979), 209–235 | DOI | MR | Zbl
[15] ter Morsche H.G., “On the Lebesque constants for cardinal $\mathcal L$-spline interpolation”, J. Approx. Theory, 45:3 (1985), 232–246 | DOI | MR | Zbl
[16] Tzimbalario J., “Lebesgue constants for cardinal $\mathcal L$-spline interpolation”, Can. J. Math., 29:2 (1977), 441–448 | DOI | MR | Zbl
[17] Kim V.A., “Tochnye konstanty Lebega dlya interpolyatsionnykh ogranichennykh $\mathcal L$-splainov tretego poryadka”, Sib. mat. zhurn., 51:2 (2010), 330–341 | MR
[18] Nguen Tkhi Tkheu Khoa, Ekstremalnye zadachi na nekotorykh klassakh gladkikh periodicheskikh funktsii, dis. d-ra fiz.-mat. nauk, MIAN im. V.A. Steklova, M., 1994, 219 pp.