We present a Chebyshev-type characterization for the best uniform approximations of periodic continuous functions by functions of the class M = ff(x) : f(x) = Z 2 0 K(x; y)h(y) dy; jh(y)j 1 a: e:; y 2 0; 2)g; where K(x; y) is a strictly cyclic variation diminishing kernel. x1 Introduction Let W r 1 a; b] be the Sobolev class of functions in C r?1 a; b] whose (r?1)st derivative is absolutely con...

We investigate the asymptotic behavior of the polynomials {Pn(f)}'t' of best uniform approximation to a function f that is continuous on a compact set K of the complex plane C and analytic in the interior of K, where K has connected complement. For example, we show that for "most" functions f, the error f -Pn(f) does not decrease faster at interior points of K than on K itself. We also describe...