a1 Florida State University Tallahassee, Florida 32306
Riemann's method for solving the Cauchy problem for hyperbolic differential equations in two independent variables has been extended in a number of papers , ,  to the wave equation in space of higher dimensions. The method, which consists in the determination of a so-called Riemann function, hinges on the solution of a characteristic value problem. Accordingly, if Riemann's method is to be used in solving a characteristic value problem, one will have to consider another characteristic value problem and thus the process becomes circular. This difficulty was first overcome by Protter  in solving the characteristic value problem for the wave equation in three variables. There he employed a variation of Riemann's method developed by Martin . Martin's result was later extended by Diaz and Martin  to the wave equation in an arbitrary number of variables. This made it possible to extend Protter's result to the wave equation in space of higher dimensions .
(Received July 06 1968)
† This research was supported by NSF research grant GP 7457.