Monatshefte für Mathematik

, Volume 112, Issue 1, pp 1–42 | Cite as

Describing functions: Atomic decompositions versus frames

  • Karlheinz Gröchenig


The theory of frames and non-orthogonal series expansions with respect to coherent states is extended to a general class of spaces, the so-called coorbit spaces. Special cases include wavelet expansions for the Besov-Triebel-Lizorkin spaces, Gabortype expansions for modulation spaces, and sampling theorems for wavelet and Gabor transforms.


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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Karlheinz Gröchenig
    • 1
  1. 1.Department of Mathematics U-9University of ConnecticutStorrsUSA

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