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In this paper we give exact values of the best $n$-term approximation widths of diagonal operators between $ell_p(mathbb{N})$ and $ell_q(mathbb{N})$ with $0<p,qleq infty$. The result will be applied to obtain the asymptotic constants of best $n$-term approximation widths of embeddings of function spaces with mixed smoothness by trigonometric system.
The present paper is concerned with new Besov-type space of variable smoothness. Nonlinear spline-approximation approach is used to give atomic decomposition of such space. Characterization of the trace space on hyperplane is also obtained.
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 smoothness parameter not larger than $1/2$. Our focus will be on the b
We study the embedding $text{id}: ell_p^b(ell_q^d) to ell_r^b(ell_u^d)$ and prove matching bounds for the entropy numbers $e_k(text{id})$ provided that $0<p<rleq infty$ and $0<qleq uleq infty$. Based on this finding, we establish optimal dimension-fr
We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes $S^r_{p,q}B(mathbb{R}^d)$ with respect to pointwise multiplication. In addition if $pleq q
The proximinality of certain subspaces of spaces of bounded affine functions is proved. The results presented here are some line