Geodesic
Gabor meets Littlewood–Paley: Gabor expansions in $L^p({{\mathbb R}}^d)$
Karlheinz Gröchenig1 ; Christopher Heil2
1Department of Mathematics The University of Connecticut Storrs, Connecticut 06269-3009, U.S.A.
2School of Mathematics Georgia Institute of Technology Atlanta, Georgia 30332-0160, U.S.A.
Studia Mathematica, Tome 146 (2001) no. 1, pp. 15-33
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm146-1-2
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

Karlheinz Gröchenig  1   ; Christopher Heil  2

1 Department of Mathematics The University of Connecticut Storrs, Connecticut 06269-3009, U.S.A.
2 School of Mathematics Georgia Institute of Technology Atlanta, Georgia 30332-0160, U.S.A. 
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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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