  We investigate properties of differential and difference operators
annihilating certain finite-dimensional subspaces of exponential functions in
two variables that are connected to the representation of real-valued
trigonometric and hyperbolic functions. Although exponential functions appear
in a variety of contexts, the motivation behind this work comes from
considering subdivision schemes with the capability of preserving those
exponential functions required for an exact description of surfaces
parametrized in terms of trigonometric and hyperbolic functions.
