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Gensun Fang

Publications and source records attributed to Gensun Fang.

5 recordsLinked to original sources
arXiv2011

Gelfand and Kolmogorov numbers of Sobolev embeddings of weighted function spaces II

We consider the Gelfand and Kolmogorov numbers of compact embeddings between weighted function spaces of Besov and Triebel-Lizorkin type with polynomial weights in the non-limiting case. Our main purpose here is to complement our previous results in \cite{ZF10} in the context of the quasi-Banach setting, $0 < p, q \le \infty$. In addition, sharp estimates for their approximation numbers in several cases left open in Skrzypczak (JAT, 2005) are provided.

math.FA↗
arXiv2011

Widths of embeddings of 2-microlocal Besov spaces

We consider the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of compact embeddings between 2-microlocal Besov spaces with weights defined in terms of the distance to a $d$-set $U\subset \mathbb{R}^n$. The sharp estimates are shown in most cases, where the quasi-Banach setting is included.

math.FA↗
arXiv2011

Widths of embeddings in weighted function spaces

We study the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of the compact embeddings of weighted function spaces of Besov and Triebel-Lizorkin type in the case where the weights belong to a large class. We obtain the exact estimates in almost all nonlimiting situations where the quasi-Banach setting is included. At the end we present complete results on related widths for polynomial weights with small perturbations, in particular the sharp estimates in the case $\alpha=d(\frac 1{p_2}-\frac 1{p_1})>0$ therein.

math.FA↗
arXiv2006

Comparison Theorems of Kolmogorov Type for Classes Defined by Cyclic Variation Diminishing Operators and Their Application

Using present a unified approach, we establish a Kolmogorov type comparison theorem for the classes of $2\pi$-periodic functions defined by a special class of operators having certain oscillation properties, which includes the classical Sobolev class of functions with 2$\pi$-periodic, the Achieser class, and the Hardy-Sobolev class as its special examples. Then, using these results, we prove a Taikov type inequality, and calculate the exact values of Kolmogorov, Gel$'$fand, linear and information $n$--widths of this class of functions in some space $L_{q}$, which is the classical Lebesgue integral space of 2$\pi$--periodic with the usual norm.

math.NA↗