Compactness criteria in function spaces

• Autorzy: Monika Dörfler , Hans G. Feichtinger , Karlheinz Gröchenig
• Języki publikacji: EN

Abstrakty

EN

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 $L²(ℝ^{d})$, and then generalized to coorbit spaces. As special cases, we obtain new characterizations of compactness in Besov-Triebel-Lizorkin, modulation and Bargmann-Fock spaces.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 46B50: Compactness in Banach (or normed) spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 94
• Numer: 1
• Strony: 37-50

Daty

wydano

2002

Twórcy

autor

Monika Dörfler

• Institut für Mathematik, Universität Wien, Strudlhofg. 4, A-1090 Wien, Austria

autor

Hans G. Feichtinger

• Institut für Mathematik, Universität Wien, Strudlhofg. 4, A-1090 Wien, Austria

autor

Karlheinz Gröchenig

• Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009, U.S.A.

Identyfikatory

DOI

10.4064/cm94-1-3