A spherical transform on Schwartz functions on the Heisenberg group associated to the action of $U(p,q)$
Volume 106 / 2006
Colloquium Mathematicum 106 (2006), 231-255
MSC: Primary 43A80; Secondary 22E25.
DOI: 10.4064/cm106-2-5
Abstract
Let $\mathcal{S}(H_{n})$ be the space of Schwartz functions on the Heisenberg group $H_{n}$. We define a spherical transform on $\mathcal{S}(H_{n})$ associated to the action (by automorphisms) of $U(p,q)$ on $H_{n}$, $p + q = n$. We determine its kernel and image and obtain an inversion formula analogous to the Godement–Plancherel formula.
