Geodesic
On Universal Sampling Recovery in the Uniform Norm
Informatics and Automation, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 213-223

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It is known that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error measured in the square norm. In this paper we demonstrate how known results on universal sampling discretization of the uniform norm and recent results on universal sampling representation allow us to provide good universal methods of sampling recovery for anisotropic Sobolev and Nikol'skii classes of periodic functions of several variables. The sharpest results are obtained in the case of functions of two variables, where the Fibonacci point sets are used for recovery.
Keywords: sampling discretization, universality, recovery. 
@article{TRSPY_2023_323_a12,
     author = {V. N. Temlyakov},
     title = {On {Universal} {Sampling} {Recovery} in the {Uniform} {Norm}},
     journal = {Informatics and Automation},
     pages = {213--223},
     publisher = {mathdoc},
     volume = {323},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2023_323_a12/}
}
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V. N. Temlyakov. On Universal Sampling Recovery in the Uniform Norm. Informatics and Automation, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 213-223. http://geodesic.mathdoc.fr/item/TRSPY_2023_323_a12/