18 citations · 18 across the 3 of their papers we have counts for
6 papers
On directional Whitney inequality
Feng Dai, Andriy Prymak
This paper studies a new Whitney type inequality on a compact domain that takes the form $$\inf_{Q\in Π_{r-1}^d({\mathcal{E}})} \|f-Q\|_p \leq C(p,r,Ω) ω_…
Entropy numbers and Marcinkiewicz-type discretization theorem
F. Dai, A. Prymak, A. Shadrin +2
This paper studies the behavior of the entropy numbers of classes of functions with bounded integral norms from a given finite dimensional linear subspace. Upper bounds of these en…
Polynomial approximation on -domains
Feng Dai, Andriy Prymak
We introduce appropriate computable moduli of smoothness to characterize the rate of best approximation by multivariate polynomials on a connected and compact -domain $Ω\subse…
On the Hadwiger covering problem in low dimensions
A. Prymak, V. Shepelska
Let be the minimal number of smaller homothetic copies of an -dimensional convex body required to cover the whole body. Equivalently, can be defined via illumination…
Christoffel function on planar domains with piecewise smooth boundary
A. Prymak, O. Usoltseva
We compute up to a constant factor the Christoffel function on planar domains with boundary consisting of finitely many curves such that each corner point of the boundary has…
Convex Multivariate Approximation by Algebras of Continuous Functions
Andriy Bondarenko, Andriy Prymak
We obtain an analog of Shvedov theorem for convex multivariate approximation by algebras of continuous functions.