Julia Sets of Orthogonal Polynomials

Jacob Stordal Christiansen; Christian Henriksen; Henrik Laurberg Petersen; Carsten Lunde Petersen

doi:10.1007/s11118-018-9687-5

Julia Sets of Orthogonal Polynomials

Jacob Stordal Christiansen, Christian Henriksen, Henrik Laurberg Petersen, Carsten Lunde Petersen

Research output: Contribution to journal › Journal article › Research › peer-review

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 fPng to properties of the support. More precisely
we relate the Julia set of Pn to the outer boundary of the support, the lled
Julia set to the polynomial convex hull K of the support, and the Green's
function associated with Pn to the Green's function for the complement
of K.

Translated title of the contribution	Juliamængder for orthogonale polynomier
Original language	English
Journal	Potential Analysis
Volume	50
Pages (from-to)	401-413
Number of pages	13
ISSN	0926-2601
DOIs	https://doi.org/10.1007/s11118-018-9687-5
Publication status	Published - 2019

Bibliographical note

Publisher's note about the attached Accepted Manuscript of the article (embargoed until february 2019): “This is a post-peer-review, pre-copyedit version of an article published in 'Potential Analysis'. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11118-018-9687-5”.

Keywords

Orthogonal Polynomials
Green's function
Julia set

Link to document

10.1007/s11118-018-9687-5

orthogonalAccepted author manuscript, 16.3 MBLicence: Unspecified

https://arxiv.org/pdf/1603.04937Licence: GNU GPL

1 Finished

Holomorpic Dynamics and Orthogonal Polynomials
Petersen, C. L., Petersen, H. L., Henriksen, C. & Christiansen, J. S.
01/11/2015 → 31/10/2018
Project: Research

Cite this

@article{48872f5a529445d48049f0a0f89c6791,

title = "Julia Sets of Orthogonal Polynomials",

abstract = "For a probability measure with compact and non-polar support in thecomplex plane we relate dynamical properties of the associated sequence oforthogonal polynomials fPng to properties of the support. More preciselywe relate the Julia set of Pn to the outer boundary of the support, the lledJulia set to the polynomial convex hull K of the support, and the Green'sfunction associated with Pn to the Green's function for the complementof K.",

keywords = "Orthogonal polynomier , Green{\textquoteright}s funktion, Julia m{\ae}ngde, Orthogonal Polynomials, Green's function, Julia set",

author = "Christiansen, {Jacob Stordal} and Christian Henriksen and Petersen, {Henrik Laurberg} and Petersen, {Carsten Lunde}",

note = "Publisher's note about the attached Accepted Manuscript of the article (embargoed until february 2019): “This is a post-peer-review, pre-copyedit version of an article published in 'Potential Analysis'. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11118-018-9687-5”.",

year = "2019",

doi = "10.1007/s11118-018-9687-5",

language = "English",

volume = "50",

pages = "401--413",

journal = "Potential Analysis",

issn = "0926-2601",

publisher = "Springer Netherlands",

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TY - JOUR

T1 - Julia Sets of Orthogonal Polynomials

AU - Christiansen, Jacob Stordal

AU - Henriksen, Christian

AU - Petersen, Henrik Laurberg

AU - Petersen, Carsten Lunde

N1 - Publisher's note about the attached Accepted Manuscript of the article (embargoed until february 2019): “This is a post-peer-review, pre-copyedit version of an article published in 'Potential Analysis'. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11118-018-9687-5”.

PY - 2019

Y1 - 2019

N2 - For a probability measure with compact and non-polar support in thecomplex plane we relate dynamical properties of the associated sequence oforthogonal polynomials fPng to properties of the support. More preciselywe relate the Julia set of Pn to the outer boundary of the support, the lledJulia set to the polynomial convex hull K of the support, and the Green'sfunction associated with Pn to the Green's function for the complementof K.

AB - For a probability measure with compact and non-polar support in thecomplex plane we relate dynamical properties of the associated sequence oforthogonal polynomials fPng to properties of the support. More preciselywe relate the Julia set of Pn to the outer boundary of the support, the lledJulia set to the polynomial convex hull K of the support, and the Green'sfunction associated with Pn to the Green's function for the complementof K.

KW - Orthogonal polynomier

KW - Green’s funktion

KW - Julia mængde

KW - Orthogonal Polynomials

KW - Green's function

KW - Julia set

U2 - 10.1007/s11118-018-9687-5

DO - 10.1007/s11118-018-9687-5

M3 - Journal article

VL - 50

SP - 401

EP - 413

JO - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

ER -

Julia Sets of Orthogonal Polynomials

Abstract

Bibliographical note

Keywords

Link to document

Holomorpic Dynamics and Orthogonal Polynomials

Cite this