Geodesic
Compactness criteria in function spaces
Monika Dörfler1 ; Hans G. Feichtinger1 ; Karlheinz Gröchenig2
1 Institut für Mathematik Universität Wien Strudlhofg. 4 A-1090 Wien, Austria
2 Department of Mathematics University of Connecticut Storrs, CT 06269-3009, U.S.A.
Colloquium Mathematicum, Tome 94 (2002) no. 1, pp. 37-50.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 ${\bf L}^2 ({\mathbb R}^d)$, and then generalized to coorbit spaces. As special cases, we obtain new characterizations of compactness in Besov–Triebel–Lizorkin, modulation and Bargmann–Fock spaces.
DOI : 10.4064/cm94-1-3
Keywords: classical criterion compactness banach spaces functions reformulated simple tightness condition time frequency domain description preserves explicitly symmetry between time frequency classical conditions result first stated proved mathbb generalized coorbit spaces special cases obtain characterizations compactness besov triebel lizorkin modulation bargmann fock spaces

Monika Dörfler 1 ; Hans G. Feichtinger 1 ; Karlheinz Gröchenig 2

1 Institut für Mathematik Universität Wien Strudlhofg. 4 A-1090 Wien, Austria
2 Department of Mathematics University of Connecticut Storrs, CT 06269-3009, U.S.A. 
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Monika Dörfler; Hans G. Feichtinger; Karlheinz Gröchenig. Compactness criteria in function spaces. Colloquium Mathematicum, Tome 94 (2002) no. 1, pp. 37-50. doi : 10.4064/cm94-1-3. http://geodesic.mathdoc.fr/articles/10.4064/cm94-1-3/

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