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Julia sets of orthogonal polynomials

Christiansen, Jacob Stordal LU ; Christian Henriksen, Christian ; Pedersen, Henrik Laurberg and Petersen, Carsten Lunde (2019) In Potential Analysis 50(3). p.401-413
Abstract
For a probability measure with compact and non-polar support in the complex plane we relate dynamical properties of the associated sequence of orthogonal polynomials {P n } to properties of the support. More precisely we relate the Julia set of P n to the outer boundary of the support, the filled Julia set to the polynomial convex hull K of the support, and the Green’s function associated with P n to the Green’s function for the complement of K.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Orthogonal polynomials, Julia set, Green’s function
in
Potential Analysis
volume
50
issue
3
pages
13 pages
publisher
Springer
external identifiers
  • scopus:85063269345
ISSN
1572-929X
DOI
10.1007/s11118-018-9687-5
language
English
LU publication?
yes
id
e27a7702-80de-43ad-93c3-b709be68a302
date added to LUP
2018-08-31 12:50:15
date last changed
2019-10-15 06:44:02
@article{e27a7702-80de-43ad-93c3-b709be68a302,
  abstract     = {For a probability measure with compact and non-polar support in the complex plane we relate dynamical properties of the associated sequence of orthogonal polynomials {P n } to properties of the support. More precisely we relate the Julia set of P n to the outer boundary of the support, the filled Julia set to the polynomial convex hull K of the support, and the Green’s function associated with P n to the Green’s function for the complement of K.},
  author       = {Christiansen, Jacob Stordal and Christian Henriksen, Christian  and Pedersen, Henrik Laurberg and Petersen, Carsten Lunde},
  issn         = {1572-929X},
  keyword      = {Orthogonal polynomials,Julia set,Green’s function},
  language     = {eng},
  number       = {3},
  pages        = {401--413},
  publisher    = {Springer},
  series       = {Potential Analysis},
  title        = {Julia sets of orthogonal polynomials},
  url          = {http://dx.doi.org/10.1007/s11118-018-9687-5},
  volume       = {50},
  year         = {2019},
}