Lagrange Interpolation Polynomials with Exponential Weights

Abstract

Let Wρ be an exponential weight of the form Wρ (t):=|t|ρ exp(-Q(t)) on ℝ := (-∞,∞), and let Ln,ρ (F,t) for F ∈ C(ℝ) be the Lagrange interpolation polynomial at the zeros {tj,n,ρ}j=1)n of the orthonormal polynomial of degree n with respect to Wρ. A new Lp -norm convergence of Ln,ρ (F,t) is discussed.