2 citations · 3 across the 5 of their papers we have counts for
5 papers
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…
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 sta…
Metric Entropy of Ellipsoids in Banach Spaces: Techniques and Precise Asymptotics
Thomas Allard, Helmut Bölcskei
We develop new techniques for computing the metric entropy of ellipsoids -- with polynomially decaying semi-axes -- in Banach spaces. Besides leading to a unified and comprehensive…
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…
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…