Advances in Computational Mathematics

, Volume 21, Issue 1–2, pp 147–180 | Cite as

Coorbit Spaces and Banach Frames on Homogeneous Spaces with Applications to the Sphere

  • Stephan Dahlke
  • Gabriele Steidl
  • Gerd Teschke


This paper is concerned with the construction of generalized Banach frames on homogeneous spaces. The major tool is a unitary group representation which is square integrable modulo a certain subgroup. By means of this representation, generalized coorbit spaces can be defined. Moreover, we can construct a specific reproducing kernel which, after a judicious discretization, gives rise to atomic decompositions for these coorbit spaces. Furthermore, we show that under certain additional conditions our discretization method generates Banach frames. We also discuss nonlinear approximation schemes based on the atomic decomposition. As a classical example, we apply our construction to the problem of analyzing and approximating functions on the spheres.

square integrable group representations time-frequency analysis atomic decompositions frames homogeneous spaces coorbit spaces modulation spaces nonlinear approximation spheres 


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Stephan Dahlke
    • 1
  • Gabriele Steidl
    • 2
  • Gerd Teschke
    • 3
  1. 1.Fachbereich Mathematik und InformatikUniversität MarburgMarburgGermany
  2. 2.Fakultät für Mathematik und InformatikUniversität MannheimMannheimGermany
  3. 3.Universität BremenBremenGermany

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