Gegenbauer Weight Functions Admitting L 2 Duffin and Schaeffer Type Inequalities

Abstract

For a given set Ω of n + 1 distinct points in [-1, 1] and algebraic polynomial Q n of degree n, sufficient conditions are found ensuring that for every other polynomial f of degree at most n the inequality |f|≤ |Q n | on Ω induces inequalities between some weighted L 2 norms of the derivatives of f and Q n