Showing math.FAShow all
3 papers · 1 filter
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.FA2024
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…
math.FA2024
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…