caa a22 4500 606244484 CHVBK 20210128101330.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s12044-015-0242-7 doi (NATIONALLICENCE)springer-10.1007/s12044-015-0242-7 Some spherical analysis related to the pairs ( U ( n ), H n ) and ( U ( p,q ), H n ), p + q [Elektronische Daten] n [SILVINA CAMPOS, LINDA SAAL] In this paper, we define the normalized spherical transform associated with the generalized Gelfand pair (U(p,q),H n ), where H n is the Heisenberg group 2n + 1-dimensional and p+q=n. We show that the normalized spherical transform F ( f ) $\mathcal {F}(f)$ of a Schwartz function f on H n restricted to the spectrum of the Gelfand pair (U(n),H n ) is the Gelfand transform ĝ $\hat {g}$ of a radial Schwartz function g on H n . Moreover, by the Godement-Plancherel inversion formula the function g can be recovered explicitly from F ( f ) $\mathcal {F}(f)$ . Indian Academy of Sciences, 2015 Heisenberg group nationallicence spherical transform nationallicence CAMPOS SILVINA Universidad Nacional de Córdoba, Córdoba, Argentina aut SAAL LINDA Universidad Nacional de Córdoba, Córdoba, Argentina aut Proceedings - Mathematical Sciences Springer India 125/3(2015-08-01), 371-397 0253-4142 125:3<371 2015 125 12044 https://doi.org/10.1007/s12044-015-0242-7 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/s12044-015-0242-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- CAMPOS SILVINA Universidad Nacional de Córdoba, Córdoba, Argentina aut NATIONALLICENCE 700 1- SAAL LINDA Universidad Nacional de Córdoba, Córdoba, Argentina aut NATIONALLICENCE 773 0- Proceedings - Mathematical Sciences Springer India 125/3(2015-08-01), 371-397 0253-4142 125:3<371 2015 125 12044