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arXiv · 2405.11066

Metric Entropy of Analytic Function Classes via Ellipsoidal Methods

Thomas Allard·Helmut Bölcskei
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Abstract

We present a systematic methodology for characterizing the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. The approach does not rely on the explicit construction of coverings or packings and yields a unified framework for deriving sharp entropy estimates for a wide range of analytic function classes, including 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 bounds in the literature.

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Thomas Allard, Helmut Bölcskei. 2024-05-17. Metric Entropy of Analytic Function Classes via Ellipsoidal Methods. https://arxiv.org/abs/2405.11066

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