Trace identities for solutions of the wave equation with initial data supported in a ball

Suppose u is the solution of the initial value problem utt −∆xu = 0, (x, t) ∈ R × [0,∞); u(x, t=0) = f(x), ut(x, t=0) = g(x), x ∈ R. Suppose n ≥ 1 is odd, f and g are supported in a ball B with boundary S, and one of f or g is zero. We derive identities relating the norm of f or g to the norm of the trace of u on S× [0,∞). These identities are derived using integral geometric and multiplier methods.