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Matrix Refinement Equations: Existence and Uniqueness.

David Colella; Christopher Heil — 1995

The journal of Fourier analysis and applications [[Elektronische Ressource]]

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

Karlheinz Gröchenig; Christopher Heil — 2001

Studia Mathematica

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.

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Matrix Refinement Equations: Existence and Uniqueness.

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

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