Quadratic Vector Equations on Complex Upper Half-plane
Author: Oskari Heikki Ajanki
Publisher:
Published: 2019
Total Pages: 133
ISBN-13: 9781470454142
DOWNLOAD EBOOK →The authors consider the nonlinear equation -\frac 1m=z+Sm with a parameter z in the complex upper half plane \mathbb H , where S is a positivity preserving symmetric linear operator acting on bounded functions. The solution with values in \mathbb H is unique and its z-dependence is conveniently described as the Stieltjes transforms of a family of measures v on \mathbb R. In a previous paper the authors qualitatively identified the possible singular behaviors of v: under suitable conditions on S we showed that in the density of v only algebraic singularities of degree two or three may occur.