相关论文: Estimates for the Gelfand widths of intersections …

Order estimates for the Kolmogorov widths of a finite-dimensional balls intersection 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 paper, order estimates for the Kolmogorov $n$-widths of an intersection of a family of balls in a mixed norm in the space $l^{m,k}_{q,\sigma}$ with $2\le q, \, \sigma <\infty$, $n\le mk/2$ are obtained.

In this paper we obtain order estimates for the Kolmogorov widths of the set $B_{p_0}^m\cap \nu B_{p_1}^m$ in $l_q^m$; here $0\le n\le m/2$, $p_0>p_1$, $q<\infty$.

In this paper, order estimates for the Kolmogorov $n$-widths of an intersection of an arbitrary family of balls $\nu_\alpha B^{\overline{k}}_{\overline{p}_\alpha}$ in $l_q^k$ are obtained for $1\le q\le 2$, $n\le \frac k2$. Here…

Order estimates for the Kolmogorov $n$-widths of $\cap _{\alpha\in A}\nu_\alpha B^{\overline{k}}_{\overline{p}}$ in $l^{\overline{k}} _{\overline{q}}$ are obtained; here $\overline{q}=(q_1, \, \dots, \, q_d)$, $2\le q_j<\infty$, $j=1, \,…

We provide sharp lower and upper bounds for the Gelfand widths of $\ell_p$-balls in the $N$-dimensional $\ell_q^N$-space for $0<p\leq 1$ and $p<q \leq 2$. Such estimates are highly relevant to the novel theory of compressive sensing, and…

We give an instability estimate for the Gel'fand inverse boundary value problem at high energies. Our instability estimate shows an optimality of several important preceeding stability results on inverse problems of such a type.

We describe the set of parameters $(p_1,p_2,q_1,q_2)$ such that the balls $B_{q_1,q_2}^{s,b}$ are rigid in $\ell_{q_1,q_2}^{s,b}$ metric i.e. they are poorly approximated by linear subspaces of dimension $\le (1-\varepsilon)sb$, for large…

Determining the maximum number of edges in an intersecting hypergraph on a fixed ground set under additional constraints is one of the central topics in extremal combinatorics. In contrast, there are few results on analogous problems…

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.

We find explicit formulas for the Hilbert series of residual intersections of a scheme in terms of the Hilbert series of its conormal modules. In a previous paper we proved that such formulas should exist. We give applications to the…

We establish formulas for bounds on the Haudorff measure of the intersection of certain Cantor sets with their translates. As a consequence we obtain a formula for the Hausdorff dimensions of these intersections.

We obtain universal affine type estimates for the location of the geometric medians of triangle perimeters and for the location of the geometric medians of triangular domains. At the end, some alternative implementations of the triangle…

We examine a Gelfand type system and show the extremal solutions are bounded provided we are close enough to the scalar case.

We prove the existence of optimal separators for intersection graphs of balls and spheres in any dimension $d$. One of our results is that if an intersection graph of $n$ spheres in $\mathbb{R}^d$ has $m$ edges, then it contains a balanced…

We prove an estimate for arbitrary measure of sections of convex bodies. The proof is based on a stability result for intersection bodies.

We provide some new estimates for distances in harmonic function spaces of several variables related to mixed norm spaces.Some of them extend previously known assertions in this direction in the unit ball and upperhalfspace.

Here we obtain order estimates for widths of weighted Sobolev classes in the weighted Lebesgue space where parameters of the second weight satisfy some limiting conditions.

We consider a finite fields version of the Erd\H{o}s-Falconer distance problem for two different sets. In a certain range for the sizes of the two sets we obtain results of the conjectured order of magnitude.