Gabor meets Littlewood–Paley:
Gabor expansions in $L^p({{\mathbb R}}^d)$
Studia Mathematica, Tome 146 (2001) no. 1, pp. 15-33
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
known gabor expansions converge unconditionally cannot characterized terms magnitudes gabor coefficients using combination littlewood paley gabor theory nevertheless characterized terms gabor expansions partial sums gabor expansions converge p norm
Affiliations des auteurs :
Karlheinz Gröchenig 1 ; Christopher Heil 2
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author = {Karlheinz Gr\"ochenig and Christopher Heil},
title = {Gabor meets {Littlewood{\textendash}Paley:
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AU - Christopher Heil
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Gabor expansions in $L^p({{\mathbb R}}^d)$
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Gabor expansions in $L^p({{\mathbb R}}^d)$
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Karlheinz Gröchenig; Christopher Heil. Gabor meets Littlewood–Paley:
Gabor expansions in $L^p({{\mathbb R}}^d)$. Studia Mathematica, Tome 146 (2001) no. 1, pp. 15-33. doi: 10.4064/sm146-1-2
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