caa a22 4500 605496080 CHVBK 20210128100534.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10231-014-0442-2 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0442-2 Paley-Wiener theorems for the $${\text {U}(n)}$$ U ( n ) -spherical transform on the Heisenberg group [Elektronische Daten] [Francesca Astengo, Bianca Di Blasio, Fulvio Ricci] We prove several Paley-Wiener-type theorems related to the spherical transform on the Gelfand pair $$\big ({H_n}\rtimes {\text {U}(n)},{\text {U}(n)}\big )$$ ( H n ⋊ U ( n ) , U ( n ) ) , where $${H_n}$$ H n is the $$2n+1$$ 2 n + 1 -dimensional Heisenberg group. Adopting the standard realization of the Gelfand spectrum as the Heisenberg fan in $$\mathbb {R}^2$$ R 2 , we prove that spherical transforms of $${\text {U}(n)}$$ U ( n ) -invariant functions and distributions with compact support in $${H_n}$$ H n admit unique entire extensions to $$\mathbb {C}^2$$ C 2 , and we find real-variable characterizations of such transforms. Next, we characterize the inverse spherical transforms of compactly supported functions and distributions on the fan, giving analogous characterizations. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Fourier transform nationallicence Schwartz space nationallicence Paley-Wiener Theorems nationallicence Heisenberg group nationallicence Astengo Francesca Dipartimento di Matematica, Via Dodecaneso 35, 16146, Genoa, Italy aut Di Blasio Bianca Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125, Milan, Italy aut Ricci Fulvio Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/6(2015-12-01), 1751-1774 0373-3114 194:6<1751 2015 194 10231 https://doi.org/10.1007/s10231-014-0442-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0442-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Astengo Francesca Dipartimento di Matematica, Via Dodecaneso 35, 16146, Genoa, Italy aut NATIONALLICENCE 700 1- Di Blasio Bianca Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125, Milan, Italy aut NATIONALLICENCE 700 1- Ricci Fulvio Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/6(2015-12-01), 1751-1774 0373-3114 194:6<1751 2015 194 10231