Geodesic
Gabor meets Littlewood–Paley: Gabor expansions in $L^p({{\mathbb R}}^d)$
Karlheinz Gröchenig1 ; Christopher Heil2
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.
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

Voir la notice de l'article

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. 
@article{10_4064_sm146_1_2,
     author = {Karlheinz Gr\"ochenig and Christopher Heil},
     title = {Gabor meets {Littlewood{\textendash}Paley:
Gabor} expansions in $L^p({{\mathbb R}}^d)$},
     journal = {Studia Mathematica},
     pages = {15--33},
     year = {2001},
     volume = {146},
     number = {1},
     doi = {10.4064/sm146-1-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm146-1-2/}
}
TY  - JOUR
AU  - Karlheinz Gröchenig
AU  - Christopher Heil
TI  - Gabor meets Littlewood–Paley:
Gabor expansions in $L^p({{\mathbb R}}^d)$
JO  - Studia Mathematica
PY  - 2001
SP  - 15
EP  - 33
VL  - 146
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm146-1-2/
DO  - 10.4064/sm146-1-2
LA  - en
ID  - 10_4064_sm146_1_2
ER  - 
%0 Journal Article
%A Karlheinz Gröchenig
%A Christopher Heil
%T Gabor meets Littlewood–Paley:
Gabor expansions in $L^p({{\mathbb R}}^d)$
%J Studia Mathematica
%D 2001
%P 15-33
%V 146
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/sm146-1-2/
%R 10.4064/sm146-1-2
%G en
%F 10_4064_sm146_1_2
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

Cité par Sources :