Gabor meets Littlewood-Paley: Gabor expansions in L-p(R-d)

Authors
Grochenig, K Heil, C
Citation
K. Grochenig et C. Heil, Gabor meets Littlewood-Paley: Gabor expansions in L-p(R-d), STUD MATH, 146(1), 2001, pp. 15-33
Citations number
19
Categorie Soggetti
Mathematics
Journal title
STUDIA MATHEMATICA
ISSN journal
00393223 → ACNP
Volume
146
Issue
1
Year of publication
2001
Pages
15 - 33
Database
ISI
SICI code
0039-3223(2001)146:1<15:GMLGEI>2.0.ZU;2-A
Abstract
It is known that Gabor expansions do not converge unconditionally in L-p an d that L-p cannot be characterized in terms of the magnitudes of Gabor coef ficients. By using a combination of Littlewood-Paley and Gabor theory, we s how 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.