max

Let 0 < < 1, 0 < ` < 1, k 1, and r be the Zolotarev sign function Z3k(;`)oftype(3k,3k 1). One finds using the Karush-Kuhn-Tucker conditions [6]thatk1 = = kM = λ. Proof of Lemma 2. Let 0 < < 1 and R: [ 1,1] [ 1,1] be a rational function. Take R(x) = R(2x 1), which is still a rational function. Without loss of generality, we can assume that R is an irreducible rational function (otherwise cancel factors till it is irreducible).