Polynomial approximation of piecewise analytic functions on arcs (Q2785843)

Let \(L\) be a Jordan arc which is divided in a finite number of subarcs, and let \(f\) be a function analytic on each (closed) subarc. Under suitable geometric conditions on \(L\), the author proves the existence of a sequence of polynomials \((p_n)\) such that \(p_n\) is ``almost best approximating'' \(f\) uniformly on \(L\) and \((p_n)\) converges pointwise more rapidly than the ``best uniform approximation'' rate to \(f\) in each point away from the division points. He thereby extends results of \textit{P. Nevai} and \textit{V. Totik} [Constructive Approximation 2, 113-127 (1986; Zbl 0604.41014)] and of \textit{E. B. Saff} and \textit{V. Totik} [J. Lond. Math. Soc., II. Ser. 39, No. 3, 487-498 (1989; Zbl 0683.41011)], who treated the special case \(L=[-1,1]\).