The Feichtinger conjecture is considered for three special families offrames. It is shown that if a wavelet frame satisfies a certain weakregularity condition, then it can be written as the finite union ofRiesz basic sequences each of which is a wavelet system. Moreover, theabove is not true for general wavelet frames. It is also shown that asup-adjoint Gabor frame can be written as the finite union of Rieszbasic sequences. Finally, we show how existing techniques can beapplied to determine whether frames of translates can be written asthe finite union of Riesz basic sequences. We end by giving an exampleof a frame of translates such that any Riesz basic subsequence mustconsist of highly irregular translates.
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