Compactness criteria in function spaces

Volume 94 / 2002

Monika Dörfler, Hans G. Feichtinger, Karlheinz Gröchenig Colloquium Mathematicum 94 (2002), 37-50 MSC: 46B50, 42B35. DOI: 10.4064/cm94-1-3

Abstract

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.

Authors

  • Monika DörflerInstitut für Mathematik
    Universität Wien
    Strudlhofg. 4
    A-1090 Wien, Austria
    e-mail
  • Hans G. FeichtingerInstitut für Mathematik
    Universität Wien
    Strudlhofg. 4
    A-1090 Wien, Austria
    e-mail
  • Karlheinz GröchenigDepartment of Mathematics
    University of Connecticut
    Storrs, CT 06269-3009, U.S.A.
    e-mail

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