Abstract
1. Main results and notations. We consider Cauchy's problem for the classical wave equation in :with initial conditions u(0, x) = uo(x) and ∂tu(0, x) = u1 (x). In (1·1) δ and m2 stand for the Laplacian in and a constant respectively. Note that a second order hyper-bolic differential equation with real constants can be reduced to (1·1) ([1], p. 183). Let uj (j = 0,1) be C∞ funotions on whose support is contained in the closed ball BR = {xεl; |x| ≥R} for some R > 0. In this note we shall show that the solution u(t, x) of (1·1) possesses the following properties.
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