48 citations · 191 across the 37 of their papers we have counts for
11 papers · 1 filter
Bounds on Kolmogorov widths and sampling recovery for classes with small mixed smoothness
V. Temlyakov, T. Ullrich
Results on asymptotic characteristics of classes of functions with mixed smoothness are obtained in the paper. Our main interest is in estimating the Kolmogorov widths of classes w…
Approximation of functions with small mixed smoothness in the uniform norm
Vladimir Temlyakov, Tino Ullrich
In this paper we present results on asymptotic characteristics of multivariate function classes in the uniform norm. Our main interest is the approximation of functions with mixed…
On optimal recovery in
V. Temlyakov
We prove that the optimal error of recovery in the norm of functions from a class $\bF$ can be bounded above by the value of the Kolmogorov width of $\bF$ in the uniform norm…
On sampling discretization in
Irina Limonova, Vladimir Temlyakov
We prove a sampling discretization theorem for the square norm of functions from a finite dimensional subspace satisfying Nikol'skii's inequality with an upper bound on the number…
A remark on entropy numbers
Vladimir Temlyakov
Talagrand's fundamental result on the entropy numbers is slightly improved. Our proof uses different ideas based on results from greedy approximation.
Sampling discretization of integral norms of the hyperbolic cross polynomials
Vladimir Temlyakov
The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. We use recent general results on sampling discretization to derive a…