Geodesic
Order estimates of the norms of derivatives of functions with zero values on linear functionals and their applications
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2017), pp. 89-95.

Voir la notice de l'article provenant de la source Math-Net.Ru

For the given finite set of linear functionals we construct functions vanishing on them and give order estimates of their derivatives. We also give their different applications.
Keywords: approximate differentiation, informative power of given functional class, computational (numerical) diameter, recovery of functions by inexact information, limiting error. 
@article{IVM_2017_3_a9,
     author = {N. Temirgaliev and A. Zhubanysheva},
     title = {Order estimates of the norms of derivatives of functions with zero values on linear functionals and their applications},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {89--95},
     publisher = {mathdoc},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_3_a9/}
}
TY  - JOUR
AU  - N. Temirgaliev
AU  - A. Zhubanysheva
TI  - Order estimates of the norms of derivatives of functions with zero values on linear functionals and their applications
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 89
EP  - 95
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_3_a9/
LA  - ru
ID  - IVM_2017_3_a9
ER  - 
%0 Journal Article
%A N. Temirgaliev
%A A. Zhubanysheva
%T Order estimates of the norms of derivatives of functions with zero values on linear functionals and their applications
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 89-95
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_3_a9/
%G ru
%F IVM_2017_3_a9
N. Temirgaliev; A. Zhubanysheva. Order estimates of the norms of derivatives of functions with zero values on linear functionals and their applications. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2017), pp. 89-95. http://geodesic.mathdoc.fr/item/IVM_2017_3_a9/

[1] Amanov T. I., “Granichnye funktsii klassov $H_{p}^{(r_1,\dots,r_n)} $ i $H_{p}^{*(r_1,\dots,r_n)} $”, Izv. AN SSSR. Ser. matem., 19:1 (1955), 17–32 | MR | Zbl

[2] Ulyanov P. L., “Vlozhenie nekotorykh klassov funktsii $H_{p}^{\omega}$”, Izv. AN SSSR. Ser. matem., 32:3 (1968), 649–686 | Zbl

[3] Temlyakov V. N., “Ob odnom prieme polucheniya otsenok snizu pogreshnostei kvadraturnykh formul”, Matem. sb., 181:10 (1990), 1403–1413

[4] Temlyakov V. N., Approximation of periodic functions, Comput. Math. and Anal. Ser., Nova Sci. Publ., 1993 | MR | Zbl

[5] Azhgaliev Sh. U., Temirgaliev N., “Ob informativnoi moschnosti lineinykh funktsionalov”, Matem. zametki, 73:6 (2003), 803–812 | DOI | MR | Zbl

[6] Zhubanysheva A. Zh., Temirgaliev N., “Informativnaya moschnost trigonometricheskikh koeffitsientov Fure i ikh predelnaya pogreshnost pri diskretizatsii operatora differentsirovaniya na mnogomernykh klassakh Soboleva”, Zhurn. vychisl. matem. i matem. fiz., 55:9 (2015), 1474–1485 | DOI | MR | Zbl

[7] Lokutsievskii O. V., Gavrikov M. B., Nachala chislennogo analiza, TOO “Yanus”, M., 1995 | MR

[8] Temirgaliev N., Kudaibergenov S. S., Shomanova A. A., “Primenenie tenzornykh proizvedenii funktsionalov v zadachakh chislennogo integrirovaniya”, Izv. RAN, Ser. matem., 73:2 (2009), 183–224 | DOI | MR | Zbl

[9] Novak E., Woźniakowski H., Tractability of multivariate problems, v. 1, EMS Tracts Math., 6, Linear information, European Math. Soc. Publishing House, Zürich, 2008 | MR | Zbl

[10] Novak E., Woźniakowski H., Tractability of multivariate problems, v. 2, EMS Tracts Math., 12, Standard information for functionals, European Math. Soc. Publishing House, Zürich, 2010 | Zbl

[11] Korneichuk N. P., Tochnye konstanty v teorii priblizheniya, Nauka, M., 1987 | MR