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A Unique Continuation Result for Klein-Gordon Bisolutions on a 2-dimensional Cylinder

C. J. Fewster
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Abstract

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 bisolution vanishes in a neighbourhood of a `sufficiently large' portion of a 2-dimensional surface lying parallel to the diagonal in the product manifold of M with itself, 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.

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C. J. Fewster. 1998-04-03. A Unique Continuation Result for Klein-Gordon Bisolutions on a 2-dimensional Cylinder. https://doi.org/10.1088/0264-9381%2F16%2F3%2F011

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