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 , and then generalized to coorbit spaces. As special cases, we obtain new characterizations of compactness in Besov-Triebel-Lizorkin, modulation and Bargmann-Fock spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-1-3,
author = {Monika D\"orfler and Hans G. Feichtinger and Karlheinz Gr\"ochenig},
title = {Compactness criteria in function spaces},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {37-50},
zbl = {1017.46014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-1-3}
}
Monika Dörfler; Hans G. Feichtinger; Karlheinz Gröchenig. Compactness criteria in function spaces. Colloquium Mathematicae, Tome 91 (2002) pp. 37-50. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-1-3/