A Result of Paley and Wiener on Damek–ricci spaces

Abstract

<jats:p>A classical result due to Paley and Wiener characterizes the existence of a nonzero function in <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" mimetype="image" xlink:href="S1446788719000077_inline1.png" /><jats:tex-math>$L^{2}(\mathbb{R})$</jats:tex-math></jats:alternatives></jats:inline-formula>, supported on a half-line, in terms of the decay of its Fourier transform. In this paper, we prove an analogue of this result for Damek–Ricci spaces.</jats:p>