DIVERGENCE OF RATIONAL APPROXIMANTS TO NON-ANALYTIC FUNCTIONS

The convergence behaviour of best uniform rational approximations with numerator degree a and denominator degree m on [-1, 11 is investigated for nonanalytic functions if ray sequences in the lower half of the Walsh table are considered, i.e. for sequences {(n, m(n))}(n=1)(infinity) with n/m(n) - c is an element of (1-infinity| as n --> infinity. For f(x) = |x|(a), a is an element of R+ \2N, it is known that the best rational approximants diverge everywhere outside [-1,1]. We investigate the situation for more general functions f that are not analytic on [-1,1].