Trigonometric quasi-greedy bases for $L^p(\bT;w)$

Details Trigonometric quasi-greedy bases for $L^p(\bT;w)$ Trigonometric quasi-greedy bases for $L^p(\bT;w)$

2006-11-28

arxiv.org/abs/math/0611892v1

Mathematics

Functional Analysis

8 pages

Scientific paper

We give a complete characterization of $2\pi$-periodic weights $w$ for which
the usual trigonometric system forms a quasi-greedy basis for $L^p(\bT;w)$,
i.e., bases for which simple thresholding approximants converge in norm. The
characterization implies that this can happen only for $p=2$ and whenever the
system forms a quasi-greedy basis, the basis must actually be a Riesz basis.

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