Metric unconditionality and Fourier analysis

Neuwirth, Stefan

Studia Mathematica, Tome 129 (1998), p. 19-62 / Harvested from The Polish Digital Mathematics Library

Résumé

We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property (umap) in terms of “block unconditionality”. Then we focus on translation invariant subspaces $L_{E}^{p} ()$ and $C_{E} ()$ of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces $p_{E} ()$ , p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between $L_{E}^{p} ()$ and $L_{E}^{p + 2} ()$ . These arithmetical conditions are used to construct counterexamples for several natural questions and to investigate the maximal density of such sets E. We also prove that if $E = {n_{k}}_{k \geq 1}$ with $| n_{k + 1} / n_{k} | \to \infty$ , then $C_{E} ()$ has umap and we get a sharp estimate of the Sidon constant of Hadamard sets. Finally, we touch on the relationship of metric unconditionality and probability theory.

Publié le : 1998-01-01

Zbl 0930.42005

EUDML-ID : urn:eudml:doc:216561

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     author = {Stefan Neuwirth},
     title = {Metric unconditionality and Fourier analysis},
     journal = {Studia Mathematica},
     volume = {129},
     year = {1998},
     pages = {19-62},
     zbl = {0930.42005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv131i1p19bwm}
}

Neuwirth, Stefan. Metric unconditionality and Fourier analysis. Studia Mathematica, Tome 129 (1998) pp. 19-62. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv131i1p19bwm/

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