Gabor meets Littlewood-Paley: Gabor expansions in Lp (Rd)

Karlheinz Gröchenig, Christopher Heil

Publications: Contribution to journalArticlePeer Reviewed

Abstract

It is known that Gabor expansions do not converge unconditionally in Lp and that Lp cannot be characterized in terms of the magnitudes of Gabor coefficients. By using a combination of Littlewood-Paley and Gabor theory, we show that Lp can nevertheless be characterized in terms of Gabor expansions, and that the partial sums of Gabor expansions converge in Lp-norm.
Original languageEnglish
Pages (from-to)15-33
Number of pages19
JournalStudia Mathematica
Volume146
Issue number1
Publication statusPublished - 2001

Austrian Fields of Science 2012

  • 1010 Mathematics

Cite this