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 L(p)-approximation order (1 less-than-or-equal-to p less-than-or-equal-to infinity) 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.