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

• Autorzy: Karlheinz Gröchenig , Christopher Heil
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42C40: Wavelets and other special systems
• 42B25: Maximal functions, Littlewood-Paley theory
• 42C15: General harmonic expansions, frames
• 46B15: Summability and bases

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 146
• Numer: 1
• Strony: 15-33

Daty

wydano

2001

Twórcy

autor

Karlheinz Gröchenig

• Department of Mathematics, The University of Connecticut, Storrs, Connecticut 06269-3009, U.S.A.

autor

Christopher Heil

• School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160, U.S.A.

Identyfikatory

DOI

10.4064/sm146-1-2