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The Journal of Geometric Analysis

, Volume 16, Issue 1, pp 53–67 | Cite as

Operators commuting with a discrete subgroup of translations

  • H. G. Feichtinger
  • H. Führ
  • K. Gröchenig
  • N. Kaiblinger
Article

Abstract

We study the structure of operators from the Schwartz space S(ℝ n ) into the tempered distributions S′(ℝ n ) that commute with a discrete subgroup of translations. The formalism leads to simple derivations of recent results about the frame operator of shift-invariant systems, Gabor, and wavelet frames.

Math Subject Classifications

Primary 47B38, 47A15 secondary 42C40 

Key Words and Phrases

Commutant shift-invariant operator shift-invariant system frame operator Walnut representation modulation invariance 

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Copyright information

© Mathematica Josephina, Inc. 2006

Authors and Affiliations

  • H. G. Feichtinger
    • 1
  • H. Führ
    • 2
  • K. Gröchenig
    • 2
  • N. Kaiblinger
    • 1
  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Institute of Biomathematics and BiometryGSF Research Center for Environment and HealthNeuherbergGermany

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