Geodesic
Uniform approximation of curvature for smooth classes of plane curves
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 273-276

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider problems of approximation of the curvature for certain smooth classes of plane curves by the curvature of elements of smooth finite-dimensional function spaces (trigonometric polynomials, splines with equidistant knots) in the uniform norm.
Keywords: curvature, uniform approximation, classes of smooth functions, trigonometric polynomials, splines with equidistant knots, estimates of approximation error. 
Yu. N. Subbotin. Uniform approximation of curvature for smooth classes of plane curves. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 273-276. http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a24/
@article{TIMM_2015_21_4_a24,
     author = {Yu. N. Subbotin},
     title = {Uniform approximation of curvature for smooth classes of plane curves},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {273--276},
     year = {2015},
     volume = {21},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a24/}
}
TY  - JOUR
AU  - Yu. N. Subbotin
TI  - Uniform approximation of curvature for smooth classes of plane curves
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2015
SP  - 273
EP  - 276
VL  - 21
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a24/
LA  - ru
ID  - TIMM_2015_21_4_a24
ER  - 
%0 Journal Article
%A Yu. N. Subbotin
%T Uniform approximation of curvature for smooth classes of plane curves
%J Trudy Instituta matematiki i mehaniki
%D 2015
%P 273-276
%V 21
%N 4
%U http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a24/
%G ru
%F TIMM_2015_21_4_a24

[1] Kolmogorov A.N., “O neravenstvakh mezhdu verkhnimi granyami posledovatelnykh proizvodnykh proizvolnoi funktsii na beskonechnom intervale”, Uch. zap. MGU, 30 (1939), 3–16

[2] Gabushin V.N., Zhiltsova O.Yu., “Otsenka krivizny razlichnykh klassov krivykh”, Problemy fiziko-matematicheskogo obrazovaniya v pedagogicheskikh vuzakh na sovremennom etape, tez. dokl., Magnitogorsk, 1996, 90

[3] Gabushin V.N., “Otsenki nekotorykh nelineinykh funktsionalov”, Izv. TulGU. Ser. Matematika, mekhanika, informatika, 12:1 (2006), 67–73 | MR

[4] Subbotin Yu.N., “Approksimatsiya krivizny gladkikh klassov ploskikh krivykh elementami konechnomernykh podprostranstv”, Izv. TulGU. Estestvennye nauki, 2012, no. 3, 41–47 | MR

[5] Tikhomirov V.M., “Poperechniki mnozhestv v funktsionalnykh prostranstvakh i teoriya nailuchshikh priblizhenii”, Uspekhi mat. nauk, 15:3 (93) (1960), 81–120 | MR | Zbl

[6] V.V. Arestov, V.I. Berdyshev, N.I. Chernykh, T.V. Demina, N.N. Kholschevnikova, S.V. Konyagin, Yu.N. Subbotin, S.A. Telyakovskii, I.G. Tsar'kov, V.A. Yudin, “Exposition of the lectures by S.B.Stechkin on approximation theory”, Eurasian Math., 2:4 (2011), 5–155 | MR | Zbl

[7] Bohr H., “Un theoreme generale sur l'integration d'un polinome trigonometric”, C.R. Acad. Sci. Paris, 200 (1935), 1276–1277

[8] Akhiezer N.I., Lektsii po teorii approksimatsii, Nauka, M., 1965, 407 pp. | MR