Compactness Criteria in Function Spaces
泛函分析
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0201161,
title = {Compactness Criteria in Function Spaces},
author = {Monika Dörfler and Hans G. Feichtinger and Karlheinz Gröchenig},
journal= {arXiv preprint arXiv:math/0201161},
year = {2007}
}