Recovering functions from the Paley-Wiener amalgam space

Abstract

In this paper we show that functions from the Paley-Wiener amalgam space $(PW,l^1)=\{f\in L^2(\mathbb{R}):\sum \Vert \hat{f}(\xi +2\pi m){\Vert }_{L^2([-\pi ,\pi ])}<\infty \}$ enjoy similar recovery properties as the classical Paley-Wiener space. Specifically, if $\{{\varphi }_{\alpha }(x):\alpha \in A\}$ is a regular family of interpolators and $\{x_n:n\in \mathbb{Z}\}$ is a complete interpolating sequence for $L^2([-\pi ,\pi ])$, then the family $\{e^{2\pi imx}{\varphi }_{\alpha }(x-x_n):m,n\in \mathbb{Z},\alpha \in A\}$ may be used to recover $f\in (PW,l^1)$.

arXiv comment5 pages

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