A spherical transform on Schwartz functions on the Heisenberg group associated to the action of
Tom 106 / 2006
Colloquium Mathematicum 106 (2006), 231-255
MSC: Primary 43A80; Secondary 22E25.
DOI: 10.4064/cm106-2-5
Streszczenie
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.
