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

Abstract

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

About 6 pages