BEST APPROXIMATION AND CYCLIC VARIATION DIMINISHING KERNELS

We study best uniform approximation of periodic functions from {integr al(0)2 pi K(x,y) h(y) dy : \h(y)\ less than or equal to 1}, where the kernel K(x,y) is strictly cyclic variatiun diminishing, and related pr oblems including periodic generalized perfect splines. For various app roximation problems of this type, we show the uniqueness of the best a pproximation and characterize the best approximation by extremal prope rties of the error function. The results are proved by using a charact erization of best approximants from quasi-Chebyshev spaces and certain perturbation results. (C) 1997 Academic Press.