Weyl quantization on compact Abelian groups and the quantum mechanics of almost periodic systems

It is shown that partial differential equations with almost periodic coefficients can be obtained by a quantization like Weyl quantization on $R^{2n}$ from Hamilton[an systems on the cotangent bundle of some infinite-dimensional manifold, the Bohr compactifieation. Hamilton[an and quantum mechanics are also constructed on the cotangent bundle of an arbitrary compact connected Abelian group.