Paley-Wiener theorems for the $${\text {U}(n)}$$ U ( n ) -spherical transform on the Heisenberg group
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| 024 | 7 | 0 | |a 10.1007/s10231-014-0442-2 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-014-0442-2 | ||
| 245 | 0 | 0 | |a Paley-Wiener theorems for the $${\text {U}(n)}$$ U ( n ) -spherical transform on the Heisenberg group |h [Elektronische Daten] |c [Francesca Astengo, Bianca Di Blasio, Fulvio Ricci] |
| 520 | 3 | |a 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. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Fourier transform |2 nationallicence | |
| 690 | 7 | |a Schwartz space |2 nationallicence | |
| 690 | 7 | |a Paley-Wiener Theorems |2 nationallicence | |
| 690 | 7 | |a Heisenberg group |2 nationallicence | |
| 700 | 1 | |a Astengo |D Francesca |u Dipartimento di Matematica, Via Dodecaneso 35, 16146, Genoa, Italy |4 aut | |
| 700 | 1 | |a Di Blasio |D Bianca |u Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125, Milan, Italy |4 aut | |
| 700 | 1 | |a Ricci |D Fulvio |u Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/6(2015-12-01), 1751-1774 |x 0373-3114 |q 194:6<1751 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0442-2 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0442-2 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Astengo |D Francesca |u Dipartimento di Matematica, Via Dodecaneso 35, 16146, Genoa, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Di Blasio |D Bianca |u Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125, Milan, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ricci |D Fulvio |u Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/6(2015-12-01), 1751-1774 |x 0373-3114 |q 194:6<1751 |1 2015 |2 194 |o 10231 | ||