Ellipsoid methods for metric entropy computation

Authors

Thomas Allard and Helmut Bölcskei

Reference

Constructive Approximation, May 2024, submitted.

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

Metric entropy, ellipsoids, complex analysis

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