Gabor meets Littlewood–Paley: Gabor expansions in Lp(Rd)
- 1 January 2001
- journal article
- research article
- Published by Institute of Mathematics, Polish Academy of Sciences in Studia Mathematica
- Vol. 146 (1) , 15-33
- https://doi.org/10.4064/sm146-1-2
Abstract
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
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