A Hilbert space of harmonic functions (Q1805025)

Let \(\widetilde M\) denote the complex light cone \(\{z \in \mathbb{C}^{n + 1} : z^2_1 + z^2_2 + \cdots + z^n_{n + 1} = 0\}\) and let \(M = \{z = x + iy \in \widetilde M : |x |= 1/2\}\). A Hilbert space of harmonic functions is constructed on \(\mathbb{R}^{n + 1}\) which is shown to be unitarily isomorphic to a subspace of \(L^2 (M)\) under the Fourier transform.