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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…
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 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…