Low regularity classes and entropy numbers

Entropy numbers of weighted Sobolev classes on the unit sphere

We obtain the asymptotic orders of entropy numbers of Sobolev classes on the unit sphere with Dunkl weight which associates with the finite reflection group. Moreover, the asymptotic order of entropy numbers of weighted Sobolev classes on the unit ball and on the standard simplex are discussed.

Estimates for the entropy numbers of the Nikol'skii-Besov classes of periodic functions of many variables in the space of quasi-continuous functions

We obtained exact-order estimates for the entropy numbers of the Nikol'skii-Besov classes $B^{\boldsymbol{r}}_{p,θ}$ of periodic functions of many variables in the metric of the space of quasi-continuous functions.

Entropy functions and functional equations

The purpose of this note is to give the general solution of two functional equations connected to the Shannon entropy and also to the Tsallis entropy. As a result of this, we present the regular solution of these equations, as well. Furthermore, we point out that the regularity assumptions used in previous works can substantially be weakened.

${\mathbb Z}_N$上傅里叶比率类的度量熵

Metric entropy of Fourier ratio classes on ${\mathbb Z}_N$

研究傅里叶比率类的度量熵，给出上下界，表明FR(f)^2作为有效维数参数，并用于均匀采样和相位轨道填充。