The Beurling-Helson theorem states that the only maps of the circle which preserve the space of absolutely convergent fourier series are affine maps. Kahane asked what happens when we relax absolute to uniform convergence; which circle maps transform absolutely convergent fourier series to uniformly convergent ones. A result of Alpar shows that any real-analytic circle map has this (Kahane) property. In higher dimensions the Kahane property can hold for some real-analytic maps and can fail for others. We will describe a simple factorisation property which gives a characterisation of those real-analytic maps between any two higher dimensional tori where the Kahane property holds.