Geodesic
Optimal subspaces for mean square approximation of classes of differentiable functions on the half-line
Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part III, Tome 539 (2024), pp. 44-65

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

We obtain sharp inequalities for the best mean square approximation of two classes of functions on the half-line, defined by boundary conditions corresponding to even and odd extension of a function. Optimal subspaces are provided by even and odd parts of the spaces generated by equidistant shifts of a single function. Under certain additional conditions on this function, the sharpness of the inequalities in the sense of average widths is proved. 
@article{ZNSL_2024_539_a2,
     author = {O. L. Vinogradov and A. Yu. Ulitskaya},
     title = {Optimal subspaces for mean square approximation of classes of differentiable functions on the half-line},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {44--65},
     publisher = {mathdoc},
     volume = {539},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_539_a2/}
}
TY  - JOUR
AU  - O. L. Vinogradov
AU  - A. Yu. Ulitskaya
TI  - Optimal subspaces for mean square approximation of classes of differentiable functions on the half-line
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2024
SP  - 44
EP  - 65
VL  - 539
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2024_539_a2/
LA  - ru
ID  - ZNSL_2024_539_a2
ER  - 
%0 Journal Article
%A O. L. Vinogradov
%A A. Yu. Ulitskaya
%T Optimal subspaces for mean square approximation of classes of differentiable functions on the half-line
%J Zapiski Nauchnykh Seminarov POMI
%D 2024
%P 44-65
%V 539
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2024_539_a2/
%G ru
%F ZNSL_2024_539_a2
O. L. Vinogradov; A. Yu. Ulitskaya. Optimal subspaces for mean square approximation of classes of differentiable functions on the half-line. Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part III, Tome 539 (2024), pp. 44-65. http://geodesic.mathdoc.fr/item/ZNSL_2024_539_a2/