Approximation and entropy numbers of composition operators

We give a survey on approximation numbers of composition operators on the Hardy space, on the disk and on the polydisk, and add corresponding new results on their entropy numbers, revealing how they are different.

Estimates of entropy numbers in probabilistic setting

In this paper, we define the entropy number in probabilistic setting and determine the exact order of entropy number of finite-dimensional space in probabilistic setting. Moreover, we also estimate the sharp order of entropy number of univariate Sobolev space in probabilistic setting by discretization method.