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arXiv · 1501.02312

Recovering functions from the modulation spaces $\mathscr{F}W$

Jeff Ledford
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Abstract

In this short note we show that functions in the modulation space $\mathscr{F}W=\{ f: \sum_{j\in\mathbb{Z}^n}\| \hat{f}(\cdot+2πj)\|_{L_\infty([-π,π]^n)}<\infty \}$ enjoy similar recovery properties as band-limited functions. If $\{ϕ_α\}$ is a regular family of cardinal interpolators, then one can build an approximand of $f$ using the fundamental functions corresponding to $ϕ_α$. Then taking the appropriate limit, one recovers $f$ both in norm and pointwise.

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Jeff Ledford. 2015-01-10. Recovering functions from the modulation spaces $\mathscr{F}W$. https://arxiv.org/abs/1501.02312

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