arXiv subjects
Publications and source records attributed to A. A. Vasil'eva.
In this paper, we obtain order estimates for the Kolmogorov widths of an intersection of a finite family of Besov classes $SB_{p_j,θ_j}^{\overline{r}_j}(\mathbb{T}^d)$ with dominating mixed smoothness in a Besov space $B_{q,σ}^{\overline{l}}(\mathbb{T}^d)$ in the case $2<q, \, σ<\infty$ when the parameters satisfy certain conditions of general position.
In the present paper we improve Besov's recent result about upper estimates for the entropy numbers of Sobolev classes on a Hölder domain (in the case when the definition of the Sobolev class involves all partial derivatives of order $r$). We also obtain upper estimates for the Kolmogorov, linear and the Gelfand widths.
Order estimates for the Kolmogorov $n$-widths of $\cap _{α\in A}ν_αB^{\overline{k}}_{\overline{p}}$ in $l^{\overline{k}} _{\overline{q}}$ are obtained; here $\overline{q}=(q_1, \, \dots, \, q_d)$, $2\le q_j<\infty$, $j=1, \, \dots, \, d$.
In this paper, order estimates for the Kolmogorov $n$-widths of an intersection of an arbitrary family of balls $ν_αB^{\overline{k}}_{\overline{p}_α}$ in $l_q^k$ are obtained for $1\le q\le 2$, $n\le \frac k2$. Here $\overline{p}_α= (p_{α,1}, \, \dots, \, p_{α,d})$, $\overline{k}=(k_1, \, \dots, \, k_d)$, $k=k_1\dots k_d$, $B^{\overline{k}}_{\overline{p}_α}$ is the unit ball with respect to the anisotropic norm given by the vector $\overline{p}_α$.
In this paper, we obtain order estimates for the Gelfand widths of intersections of finite-dimensional balls under some conditions on parameters.
In this article, order estimates for the Kolmogorov widths of periodic anisotropic Sobolev and Nikol'skii classes are obtained, as well as order estimates for the Kolmogorov widths of anisotropic finite-dimensional balls.
In this paper, we obtain order estimates for the Kolmogorov widths of periodic Sobolev classes with restictions on derivatives of order $r_j$ with respect to $j$th variable in metrics $L_{p_j}$ ($1\le j\le d$).
In this paper, order estimates for the Kolmogorov $n$-widths of an intersection of a family of balls in a mixed norm in the space $l^{m,k}_{q,σ}$ with $2\le q, \, σ<\infty$, $n\le mk/2$ are obtained.
Order estimates for the Kolmogorov widths of an intersection of two finite-dimensional balls in a mixed norm under some conditions on the parameters are obtained.
In this article, we obtain the order estimates for the Kolmogorov widths of sets with conditions on the norm in the weighted Sobolev space $W^r_{p_1}$ and in the weighted space $L_{p_0}$.
Order estimates for the Kolmogorov widths of a finite-dimensional balls intersection are obtained.
In this paper order estimates for the Kolmogorov widths of weighted Sobolev classes on a multi-dimensional domain are obtained. The classes are defined by conditions on the highest-order derivatives and the derivative of order zero.
In this paper we obtain order estimates for the Kolmogorov widths of the set $B_{p_0}^m\cap νB_{p_1}^m$ in $l_q^m$; here $0\le n\le m/2$, $p_0>p_1$, $q<\infty$.
In this paper order estimates for the linear widths of some function classes are obtained; these classes are defined by restrictions on the weighted $L_{p_1}$-norm of the r-th derivative and the weighted $L_{p_0}$-norm of zero derivative.
In this paper we prove that Kolmogorov widths of weighted Sobolev classes with restrictions $f(a)=\dots=f^{(k-1)}(a)=f^{(k)}(b)=\dots=f^{(r-1)}(b)=0$ in a weighted Lebesgue space and spectral numbers of some non-linear differential equation coincide. Here we suppose that the embedding is compact.
In this paper, estimates for norms of weighted summation operators (discrete Hardy-type operators) on a tree are obtained for $1<p<q<\infty$ and for arbitrary weights and trees.
In this paper we obtain order estimates for entropy numbers of embeddings of weighted Sobolev spaces into weighted Lebesgue spaces and of weighted summation operators on trees. Here we consider some critical conditions on the parameters.
In this paper order estimates for entropy numbers of embeddings of weighted Sobolev spaces on a John domain are obtained. In addition, we obtain order estimates for entropy numbers of summation operators on trees.