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The Feichtinger Conjecture for Wavelet Frames, Gabor Frames and Frames of Translates |
Canad. J. Math. 58(2006), 1121-1143
Published:2006-12-01
Printed: Dec 2006
Printed: Dec 2006
- Marcin Bownik
- Darrin Speegle
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 |
| MSC Classifications: |
42B25 - Maximal functions, Littlewood-Paley theory 42B35 - Function spaces arising in harmonic analysis 42C40 - Wavelets and other special systems |