Quadratic Vector Equations on Complex Upper Half-Plane

by Laszlo Erdos, Oskari Heikki Ajanki, Torben Kruger

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...

• Format: Paperback
• Language: English
• ISBN: 1470436833
• ISBN13: 9781470436834
• Release Date: December 2019
• Publisher: American Mathematical Society
• Length: 133 Pages