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.

翻译：我们调查差异操作员和差异操作员的特性,在两个变量中消除指数函数的某些有限维次空间,这两个变量与实际价值三角函数和双曲函数的表示相关。 虽然指数函数出现在多种情况下,但这项工作背后的动机在于考虑子系统,以便保留精确描述三角函数和双曲函数的平衡表面所需的指数函数。