Continuous Frames , Function Spaces , and the Discretization Problem

@inproceedings{Fornasier2005ContinuousF,
  title={Continuous Frames , Function Spaces , and the Discretization Problem},
  author={Massimo Fornasier and Holger Rauhut and Karlheinz Gr{\"o}chenig},
  year={2005}
}
A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function spaces can be identified as such spaces. We provide a general method to derive Banach frames and atomic decompositions for these Banach spaces by sampling the continuous frame. This is done by generalizing the coorbit space theory developed by Feichtinger and… CONTINUE READING
Highly Cited
This paper has 24 citations. REVIEW CITATIONS

References

Publications referenced by this paper.
Showing 1-10 of 50 references

Foundations of Time-Frequency Analysis, Birkhäuser Verlag

  • K. Gröchenig
  • 2001
Highly Influential
8 Excerpts

Banachräume Glatter Funktionen und Zerlegungs-Methoden, Ph.D. thesis, University of Vienna

  • P. Gröbner
  • 1992
Highly Influential
5 Excerpts

On the regular representation of a nonunimodular locally compact group

  • M. Duflo, C. C. Moore
  • J. Funct. Anal
  • 1976
Highly Influential
4 Excerpts

An interpolation family between Gabor and wavelet transformations. Application to differential calculus and construction of anisotropic Banach spaces, in Adv

  • M. Holschneider, B. Nazaret
  • In Partial Diff. Eq., Nonlinear Hyperbolic…
  • 2003
Highly Influential
5 Excerpts

Embeddings and uncertainty principles for generalized modulation spaces, Chapter 4 in Modern Sampling Theory: Mathematics and Applications, Benedetto, J.J

  • J. A. Hogan, J. D. Lakey
  • 2000
Highly Influential
5 Excerpts

Describing functions: Atomic decompositions versus frames, Monatsh

  • K. Gröchenig
  • 1991
Highly Influential
11 Excerpts

Banach spaces related to integrable group representations and their atomic decompositions I

  • H. G. Feichtinger, K. Gröchenig
  • J. Funct. Anal
  • 1989
Highly Influential
11 Excerpts

Banach spaces related to integrable group representations and their atomic decompositions II, Monatsh

  • H. G. Feichtinger, K. Gröchenig
  • 1989
Highly Influential
11 Excerpts

Similar Papers

Loading similar papers…