Fixed points of conjugated Blaschke products with applications to gravitational lensing
type: Item
instance of: scholarly article
title: Fixed points of conjugated Blaschke products with applications to gravitational lensing
zbMATH Open document ID: 1193.30033
DOI: 10.1007/BF03321738
author: Ludwig Kuznia
author: Erik Lundberg
published in: Computational Methods and Function Theory
publication date: 2009-12-15T00:00:00Z
review text: A conjecture in astronomy was recently resolved as an accidental corollary to a theorem regarding zeros of certain planar harmonic maps. As a step towards an extension of the fundamental theorem of algebra, the theorem gives a bound of \(5n-5\) for the number of zeros of a function of the form \(r(z) - \bar z\), where \(r(z)\) is rational of degree \(n\). In the paper under review, the authors investigate the case when \(r(z)\) is a Blaschke product. The resulting (sharp) bound is \(n+3\), and the proof is simple. They also discuss an application to gravitational lenses consisting of collinear point masses.
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 83C99
Mathematics Subject Classification ID: 26C15
zbMATH DE Number: 5648467
zbMATH Keywords: Blaschke product
zbMATH Keywords: gravitational lens
zbMATH Keywords: collinear point masses
zbMATH Keywords: proper self-maps
reviewed by: Zengjian Lou
MaRDI profile type: Publication
cites work: Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field
cites work: On the number of zeros of certain rational harmonic functions
cites work: Q3588172
cites work: Boundary interpolation with Blaschke products of minimal degree
cites work: The valence of harmonic polynomials
description: scientific article; zbMATH DE number 5648467