Wavelets as unconditional bases in \(L_p(\mathbb{R})\). (English) Zbl 1055.42509
The author presents weak conditions on the decay of a wavelet so that the wavelet basis is an unconditional basis in \(L_p (\mathbb{R})\), \(1 < p < \infty\). He also shows that a certain class of unimodular wavelets (also referred to as minimally supported frequency or \(s\)-wavelets) yields unconditional bases in \(L_p (\mathbb{R})\), \(1 < p < \infty\).
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 46B15 | Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
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