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$$u_{tt} - \Delta_{x} u = 0, \quad (x,t) \in R^{n} {\times}[0, \infty)$$$$u(x, t = 0)=f(x), \quad u_{t}(x, t = 0) = g(x), \quad x \in R^{n}$$ 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. Copyright © 2005 John Wiley & Sons, Ltd.