English

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.

Keywords

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}
}
R2 v1 2026-06-28T16:31:26.262Z