Paley-Wiener theorems for the \(\mathrm U(n)\)-spherical transform on the Heisenberg group (Q893373)

The authors prove several Paley-Wiener-type theorems related to the spherical transform on the Gelfand pair \((\mathbb{H}^n \rtimes U(n),\;U(n))\), where \(\mathbb{H}^n\) is the \((2n+1)\)-dimensional Heisenberg group. The authors first prove real Paley-Wiener theorems for the direct spherical transform. In the second part of the paper, the authors show a Paley-Wiener theorem for the inverse spherical transform.