An Analytic and Numerical Analysis of Weighted Singular Cauchy Integrals with Exponential Weights on ℝ. (29th September 2022)

• Record Type: Journal Article
• Authors: Damelin, Steven B.; Diethelm, Kai
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 13(2022)
• Page Start: 1538
• Page End: 1577
• Publication Date: 2022-09-29
• Subjects: Cauchy principal value integral -- Erdős weight -- exponential weight -- Freud weight -- numerical approximation -- orthogonal polynomial -- quadrature -- singular integral -- weighted approximation; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2112051
• Languages: English
• ISSNs: 0163-0563

Abstract

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 .