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

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

1998-04-03

arxiv.org/abs/gr-qc/9804011v1

Class.Quant.Grav.16:789-796,1999

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX2e, 9 pages

Scientific paper

10.1088/0264-9381/16/3/011

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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