Interpolation via symmetric exponential functions

Complex valued functions on the Euclidean space n, symmetric or antisymmetric with respect to the permutation group Sn, are often dealt with in various branches of physics, such as quantum theory or theory of integrable systems. One often needs to approximate such functions with series consisting of various special functions which satisfy nice properties. Questions of uniform convergence of such approximations are crucial for applications. In this article a family of special functions called the symmetric exponential functions are used for such approximation and the uniform convergence of their sums is considered.