Geodesic
Sampling Discretization of Integral Norms and Its Application
Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 106-119

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

The paper addresses a problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under two standard kinds of assumptions: conditions on the entropy numbers and conditions in terms of Nikol'skii-type inequalities. We prove some upper bounds on the number of sample points sufficient for good discretization and show that these upper bounds are sharp in a certain sense. Then we apply our general conditional results to subspaces with special structure, namely, subspaces with tensor product structure. We demonstrate that the application of theorems based on Nikol'skii-type inequalities provides somewhat better results than the application of theorems based on entropy numbers conditions. Finally, we apply discretization results to the problem of sampling recovery.
Keywords: sampling discretization, entropy numbers, Nikol'skii inequality, recovery. 
@article{TRSPY_2022_319_a8,
     author = {F. Dai and V. N. Temlyakov},
     title = {Sampling {Discretization} of {Integral} {Norms} and {Its} {Application}},
     journal = {Informatics and Automation},
     pages = {106--119},
     publisher = {mathdoc},
     volume = {319},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a8/}
}
TY  - JOUR
AU  - F. Dai
AU  - V. N. Temlyakov
TI  - Sampling Discretization of Integral Norms and Its Application
JO  - Informatics and Automation
PY  - 2022
SP  - 106
EP  - 119
VL  - 319
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a8/
LA  - ru
ID  - TRSPY_2022_319_a8
ER  - 
%0 Journal Article
%A F. Dai
%A V. N. Temlyakov
%T Sampling Discretization of Integral Norms and Its Application
%J Informatics and Automation
%D 2022
%P 106-119
%V 319
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a8/
%G ru
%F TRSPY_2022_319_a8
F. Dai; V. N. Temlyakov. Sampling Discretization of Integral Norms and Its Application. Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 106-119. http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a8/