Approximation by Piecewise Exponentials *

A function is called an exponential if it is a linear combination of products of polynomials with pure exponentials. In this paper lower and upper bounds for families of spaces of piecewise exponentials are established. In particular, the exact Lp-approximation order (1 _< p _<) is found for a family {Sh}h>O of function spaces when each Sh is generated by an exponential box spline and its multi-integer translates.