Ellipsoid Methods for Metric Entropy Computation
Functional Analysis
2024-05-21 v1 Complex Variables
Abstract
We present a new methodology for the characterization of the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. This procedure does not rely on the explicit construction of coverings or packings and provides a unified framework for the derivation of the metric entropy of a wide variety of analytic function classes, such as periodic functions analytic on a strip, analytic functions bounded on a disk, and functions of exponential type. In each of these cases, our results improve upon the best known results in the literature.
Cite
@article{arxiv.2405.11066,
title = {Ellipsoid Methods for Metric Entropy Computation},
author = {Thomas Allard and Helmut Bölcskei},
journal= {arXiv preprint arXiv:2405.11066},
year = {2024}
}