Compactness Criteria in Function Spaces

Details Compactness Criteria in Function Spaces Compactness Criteria in Function Spaces

2002-01-17

arxiv.org/abs/math/0201161v1

Mathematics

Functional Analysis

Scientific paper

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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