Localized frames are finite unions of Riesz sequences. (English) Zbl 1019.42019
Feichtinger conjectured that every frame can be decomposed into a finite union of Riesz sequences. While the full conjecture remains open, the author proves it for frames satisfying a certain localization property. This abstract condition turns out to be satisfied for (irregular) Gabor systems generated by a function in a specified modulation space, and for the reproducing kernel frame associated to a shift-invariant space.
Reviewer: Ole Christensen (Lyngby)
MSC:
42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
42C15 | General harmonic expansions, frames |