Solution of the wave equation in Rn + 1 with data on a characteristic cone

Abstract

A unified treatment of the problem is presented for both odd and even space dimensions. In contrast to previous results for odd n, when the space dimension is even, there is no general existence although the uniqueness holds. A necessary and sufficient condition for admissible data is given. Of independent interest are several versions of the “Plancherel theorem” of the Radon transform, in the space L 2 1( R n ) of all functions whose gradients are square integrable.