Approximation by Piecewise Exponentials

Abstract

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 $L_p $-approximation order $(1 \leq p \leq \infty )$ is found for a family $\{ {S_h } \}_{h > 0} $ of function spaces when each $S_h$ is generated by an exponential box spline and its multi-integer translates.