Gabor meets Littlewood-Paley: Gabor expansions in $L^{p}(ℝ^{d})$

Karlheinz Gröchenig; Christopher Heil

Gabor meets Littlewood-Paley: Gabor expansions in

L^{p} (ℝ^{d})

Karlheinz Gröchenig ; Christopher Heil

Studia Mathematica, Tome 147 (2001), p. 15-33 / Harvested from The Polish Digital Mathematics Library

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Résumé

It is known that Gabor expansions do not converge unconditionally in $L^{p}$ and that $L^{p}$ cannot be characterized in terms of the magnitudes of Gabor coefficients. By using a combination of Littlewood-Paley and Gabor theory, we show that $L^{p}$ can nevertheless be characterized in terms of Gabor expansions, and that the partial sums of Gabor expansions converge in $L^{p}$ -norm.

Publié le : 2001-01-01

Zbl 0970.42021

EUDML-ID : urn:eudml:doc:284992

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     title = {Gabor meets Littlewood-Paley: Gabor expansions in $L^{p}($\mathbb{R}$^{d})$
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     year = {2001},
     pages = {15-33},
     zbl = {0970.42021},
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Karlheinz Gröchenig; Christopher Heil. Gabor meets Littlewood-Paley: Gabor expansions in $L^{p}(ℝ^{d})$
            . Studia Mathematica, Tome 147 (2001) pp. 15-33. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-1-2/