Geodesic
Estimates of functionals by the second moduli of continuity of even derivatives
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 41, Tome 416 (2013), pp. 70-90

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

We establish an expansion of a function in terms of the second order differences of its derivatives. This expansion generalizes the well-known expansion in terms of the first order differences. Then, with the help of this expansion, we estimate some functionals by the second moduli of continuity. As particular cases of the estimates obtained, we have Jackson-type inequalities for approximations by entire fuctions of exponential type, trigonometric polynomials and splines in various function spaces. The constants in the new inequalities are smaller than those known before. 
@article{ZNSL_2013_416_a2,
     author = {O. L. Vinogradov and V. V. Zhuk},
     title = {Estimates of functionals by the second moduli of continuity of even derivatives},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {70--90},
     publisher = {mathdoc},
     volume = {416},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a2/}
}
TY  - JOUR
AU  - O. L. Vinogradov
AU  - V. V. Zhuk
TI  - Estimates of functionals by the second moduli of continuity of even derivatives
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2013
SP  - 70
EP  - 90
VL  - 416
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a2/
LA  - ru
ID  - ZNSL_2013_416_a2
ER  - 
%0 Journal Article
%A O. L. Vinogradov
%A V. V. Zhuk
%T Estimates of functionals by the second moduli of continuity of even derivatives
%J Zapiski Nauchnykh Seminarov POMI
%D 2013
%P 70-90
%V 416
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a2/
%G ru
%F ZNSL_2013_416_a2
O. L. Vinogradov; V. V. Zhuk. Estimates of functionals by the second moduli of continuity of even derivatives. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 41, Tome 416 (2013), pp. 70-90. http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a2/