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Compactness Criteria in Function Spaces

Monika Dörfler·Hans G. Feichtinger·Karlheinz Gröchenig
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Abstract

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(R^d), and then generalized to coorbit spaces. As special cases, we obtain new characterizations of compactness in Besov-Triebel-Lizorkin spaces, modulation spaces and Bargmann-Fock spaces.

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Monika Dörfler, Hans G. Feichtinger, Karlheinz Gröchenig. 2002-01-17. Compactness Criteria in Function Spaces. https://arxiv.org/abs/math/0201161

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