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The Feichtinger Conjecture for Wavelet Frames, Gabor Frames and Frames of Translates

  Published:2006-12-01
 Printed: Dec 2006
  • Marcin Bownik
  • Darrin Speegle
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Abstract

The Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a sup-adjoint Gabor frame can be written as the finite union of Riesz basic sequences. Finally, we show how existing techniques can be applied to determine whether frames of translates can be written as the finite union of Riesz basic sequences. We end by giving an example of a frame of translates such that any Riesz basic subsequence must consist of highly irregular translates.
Keywords: frame, Riesz basic sequence, wavelet, Gabor system, frame of translates, paving conjecture frame, Riesz basic sequence, wavelet, Gabor system, frame of translates, paving conjecture
MSC Classifications: 42B25, 42B35, 42C40 show english descriptions Maximal functions, Littlewood-Paley theory
Function spaces arising in harmonic analysis
Wavelets and other special systems
42B25 - Maximal functions, Littlewood-Paley theory
42B35 - Function spaces arising in harmonic analysis
42C40 - Wavelets and other special systems
 

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