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eiKr u(r, O)-(K f(O1/2 f(O) + 0 ?O2) Kr--*oo (Kr)" where f(0) is a continuous function of 0. This radiation condition is more explicit than the usual Sommerfeld condition, and, by its very nature, rules out surface waves as they are oscillating and nondecaying along the boundary. It was found to be equally convenient to state and prove uniqueness for all N and Xrn# ?iK. The explicit far field behavior mentioned above is not required; rather we assume a Sommerfeld condition. Hence, where we overlap with Kane [3], the required radiation condition is improved and the theorem is extended for higher order boundary conditions. Otherwise, in the case where surface waves arise, the results are independent.

Uniqueness theorem for the reduced wave equation under an $N$th order differential boundary condition