An Analytic and Numerical Analysis of Weighted Singular Cauchy Integrals with Exponential Weights on ℝ

Abstract

This article concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights with finite moments and with smooth external fields with varying smooth convex rate of increase for large argument. Our analysis relies in part on weighted polynomial interpolation at the zeros of orthonormal polynomials with respect to w 2. We also study bounds for the first derivatives of a class of functions of the second kind for w 2.