most citedMetric Entropy of Analytic Function Classes via Ellipsoidal Methods

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math.FA2026★ 1 cited

Metric Entropy of Analytic Function Classes via Ellipsoidal Methods

Thomas Allard, Helmut Bölcskei

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 th…

math.FA2026

Entropy and Minimax Risk of Hypoelliptic Pseudodifferential Operators

Thomas Allard, Helmut Bölcskei

We characterize the entropy and minimax risk of a broad class of compact pseudodifferential operators. Under suitable decay and regularity conditions on the symbol, we combine a We…

math.ST2025

Metric Entropy and Minimax Risk of Ellipsoids with an Application to Pinsker's Theorem

Thomas Allard

We study how large an ellipsoid is by introducing type- integrals that capture the average decay of its semi-axes. These integrals turn out to be closely related to st…

math.FA2025

Entropy of Compact Operators with Applications to Landau-Pollak-Slepian Theory and Sobolev Spaces

Thomas Allard, Helmut Bölcskei

We derive a precise general relation between the entropy of a compact operator and its eigenvalues. It is then shown how this result along with the underlying philosophy can be app…