BEST APPROXIMATION BY PERIODIC SMOOTH FUNCTIONS

Let (W) over tilde(n) be the set of 2 pi-periodic functions with absol utely continuous (n-1)th derivatives and nth derivatives with essentia l suprema bounded by one. Let n > 1. Best uniform approximations to a periodic continuous function from (W) over tilde(n) are characterized. The result depends upon an analysis of the relation between the zeros , knots, and signs of periodic splines with simple knots. An appendix by O. V. Davydov states an alternative characterisation and demonstrat es that the two characterisations are equivalent. (C) 1998 Academic Pr ess.