The Klein-Gordon operator in conformal space

We consider the Minkowski space M₄ as a local chart of a compact differentiable pseudo-Riemannian manifold M⁴_c, on which the whole conformal group $\text{O(2, 4)}\text{Z}{}_2$ acts continuously. We investigate the conditions under which functions or differential operators on the space M₄ can be uniquely continued to the conformal manifold M⁴_c. This is done by using methods well-known in the theory of differentiable manifolds. In particular, we show that the Klein-Gordon operator □+m² can be uniquely continued to the space M⁴_c and we discuss the conformal invariance of the Klein-Gordon equation on the manifold M⁴_c.