A maximum property is obtained for the solutions of the odd-dimensional wave equation in the interior of the characteristic cone. In this note we will establish a maximum principle for the odd-dimen- The method of M. Riesz shows that u(X, t) = EMLTítS; X, r] is the solution of the problem Da = 0 in t > |X| with u(X, |X|) = cp(X). 77 License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use 78 H. RHEE EU[i-l)k; X, t] = T2U + 1)/T\2k + 2). Hence we

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... have the following maximum principle. Theorem. Suppose that Dzz = 0 in t > \X\ and that uiX, r) < M. If (kl)-l8k+lir"-?>uiX, r)) -uiX, r) < 0, then uiX, t) < M for n = 3, uiX,t) < M for 72 > 5 in t > \X\.