Bounds for Entropy Numbers of Some Critical Operators

TL;DR

This paper establishes new upper bounds for entropy numbers of specific operators, including summation on binary trees and Volterra integral operators, especially in critical cases where existing methods fail.

Contribution

It introduces a novel method to estimate entropy numbers in critical cases, expanding the analytical tools available for such operators.

Findings

Derived upper bounds for entropy numbers in critical cases

Developed a new method applicable to challenging operator classes

Potential for further applications of the new approach

Abstract

We provide upper bounds for entropy numbers for two types of operators: summation operators on binary trees and integral operators of Volterra type. Our efforts are concentrated on the critical cases where none of known methods works. Therefore, we develop a method which seems to be completely new and probably merits further applications.