Entropy of compact operators with applications to Landau-Pollak-Slepian theory and Sobolev spaces

Authors

Thomas Allard and Helmut Bölcskei

Reference

Applied and Computational Harmonic Analysis, June 2024, submitted.

Abstract

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 applied to improve substantially on the best known characterizations of the entropy of the Landau-Pollak-Slepian operator and the metric entropy of unit balls in Sobolev spaces.

Keywords

Entropy of compact operators, ellipsoids, sampling theory, Landau-Pollak-Slepian operator, Weyl's law, Sobolev spaces

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