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

Karlheinz Gröchenig, and Christopher Heil. "Gabor meets Littlewood-Paley: Gabor expansions in $L^{p}(ℝ^{d})$." Studia Mathematica 146.1 (2001): 15-33. <http://eudml.org/doc/284992>.

@article{KarlheinzGröchenig2001,
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.},
author = {Karlheinz Gröchenig, Christopher Heil},
journal = {Studia Mathematica},
keywords = {frames; Gabor expansions; Gabor frames; Littlewood-Paley theory; modulation space; phase space; time-frequency analysis; Walnut representation},
language = {eng},
number = {1},
pages = {15-33},
title = {Gabor meets Littlewood-Paley: Gabor expansions in $L^\{p\}(ℝ^\{d\})$},
url = {http://eudml.org/doc/284992},
volume = {146},
year = {2001},
}

TY - JOUR
AU - Karlheinz Gröchenig
AU - Christopher Heil
TI - Gabor meets Littlewood-Paley: Gabor expansions in $L^{p}(ℝ^{d})$
JO - Studia Mathematica
PY - 2001
VL - 146
IS - 1
SP - 15
EP - 33
AB - 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.
LA - eng
KW - frames; Gabor expansions; Gabor frames; Littlewood-Paley theory; modulation space; phase space; time-frequency analysis; Walnut representation
UR - http://eudml.org/doc/284992
ER -