Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Metric unconditionality and Fourier analysis

100%

Neuwirth S.

Studia Mathematica

1998

tom 131

nr 1

19-62

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 $L^{p}_{E}(𝕋)$ and $C_{E}(𝕋)$ of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces $p_{E}(𝕋)$, p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between $L^{p}_{E}(𝕋)$ and $L^{p+2}_{E}(𝕋)$. 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 $E = {n_k}_{k≥1}$ with $|n_{k+1}/n_k| → ∞$, then $C_{E}(𝕋)$ 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.

Ograniczanie wyników

1 Studia Mathematica

1 Neuwirth S.

1 1998

Wyniki wyszukiwania

Metric unconditionality and Fourier analysis