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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
; ; and
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
2022-04-25 08:29:18
@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}},
  keywords     = {{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}},
  doi          = {{10.1007/s11118-018-9687-5}},
  volume       = {{50}},
  year         = {{2019}},
}