A pr 1 99 8 A Unique Continuation Result for Klein – Gordon Bisolutions on a 2 - dimensional Cylinder

We prove a novel unique continuation result for weak bisolutions to the massive Klein–Gordon equation on a 2-dimensional cylinder M. Namely, if such a bisolu-tion vanishes in a neighbourhood of a 'sufficiently large' portion of a 2-dimensional surface lying parallel to the diagonal in M ×M , then it is (globally) translationally invariant. The proof makes use of methods drawn from Beurling's theory of interpolation. An application of our result to quantum field theory on 2-dimensional cylinder spacetimes will appear elsewhere.