This is an announcement for the paper "Trigonometric quasi-greedy bases for $L^p(\bT;w)$" by Morten Nielsen.

Abstract: 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.

Archive classification: Functional Analysis

Mathematics Subject Classification: 42C15

Remarks: 8 pages

The source file(s), trig_quasi_greedy.tex: 23971 bytes, is(are) stored in gzipped form as 0611892.gz with size 8kb. The corresponding postcript file has gzipped size 98kb.

Submitted from: mnielsen@math.wustl.edu

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