An Analytic and Numerical Analysis of Weighted Singular Cauchy Integrals with Exponential Weights on ℝ. (29th September 2022) - Damelin, Steven B.; Diethelm, Kai
Abstract: This article concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights w : = exp ( − Q ) with finite moments and with smooth external fields Q : R → [ 0, ∞ ), 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 .