Quadratic differentials A(z-a)(z-b)dz²/(z-c)² and algebraic Cauchy transform

2015/06/22 by Mohamed Jalel Atia, Atia, Mohamed Jalel, Faouzi Thabet +1
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical functions and polynomials #Polynomial and algebraic computation #math.CA

paper · pdf · doi:10.48550/arxiv.1506.06543

13 pages, 8 figures

openalex publication_date 2015/06/22 · arxiv created 2016/02/19 · arxiv updated 2016/02/22 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we discuss the representability almost everywhere (a.e.) in the plane of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite number of isolated points. We discuss the existence of critical trajectories of a family of quadratic differentials.

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