We prove the Paley-Wiener theorem for the Helgason Fourier transform of smooth compactly supported 𝔳-radial functions on a Damek-Ricci space S = NA.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6647-11-2015, author = {Roberto Camporesi}, title = {The v-radial Paley-Wiener theorem for the Helgason Fourier transform on Damek-Ricci spaces}, journal = {Colloquium Mathematicae}, volume = {144}, year = {2016}, pages = {87-113}, zbl = {06574994}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6647-11-2015} }
Roberto Camporesi. The 𝔳-radial Paley-Wiener theorem for the Helgason Fourier transform on Damek-Ricci spaces. Colloquium Mathematicae, Tome 144 (2016) pp. 87-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6647-11-2015/