Julia sets of orthogonal polynomials
(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:
https://lup.lub.lu.se/record/e27a7702-80de-43ad-93c3-b709be68a302
- author
- Christiansen, Jacob Stordal LU ; Christian Henriksen, Christian ; Pedersen, Henrik Laurberg and Petersen, Carsten Lunde
- organization
- publishing date
- 2019
- 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}}, }