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Compactness criteria in function spaces

Monika DörflerHans G. FeichtingerKarlheinz Gröchenig — 2002

Colloquium Mathematicae

The classical criterion for compactness in Banach spaces of functions can be reformulated into a simple tightness condition in the time-frequency domain. This description preserves more explicitly the symmetry between time and frequency than the classical conditions. The result is first stated and proved for L ² ( d ) , and then generalized to coorbit spaces. As special cases, we obtain new characterizations of compactness in Besov-Triebel-Lizorkin, modulation and Bargmann-Fock spaces.

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