Abstract
Abstract 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.
Highlights
This paper surveys results on approximation numbers of composition operator on the Hardy space, and gives new results, on their entropy numbers, in one or several dimensions
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 di erent
With T = Cφ, namely T(f ) = f ◦ φ where φ is an analytic self-map of the polydisk DN, the situation is slightly di erent
Summary
This paper surveys results on approximation numbers of composition operator on the Hardy space, and gives new results, on their entropy numbers, in one or several dimensions. For any non-constant analytic map φ : D → D, we have: nl→im∞[an(Cφ)] /n = exp − /Cap [φ(D)] , where Cap [φ(D)] is the Green capacity of φ(D), from which it follows that limn→∞[an(Cφ)] /n =
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