2024/05/17 by Thomas Allard, Helmut Bölcskei, Allard, Thomas +1
Computer Science · Physics and Astronomy · #30E10 #41A46 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2405.11066
openalex publication_date 2024/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.