Characterization of weights in best rational weighted approximation of piecewise smooth functions. I (Q1824785)

A complex rational weighted \(L^ p\)-approximation \((0<p\leq \infty)\) of piecewise analytic functions on [0,1] is considered. Those weights that allow exponential order of approximation in this setting are characterized. This is a generalization of Newman's original work for uniform approximation of \(| x|\) on [-1,1] by rationals and also, could be of benefit for recursive digital filter, as the authors note.