Julia Sets of Orthogonal Polynomials

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

doi:10.1007/s11118-018-9687-5

Julia Sets of Orthogonal Polynomials

Jacob Stordal Christiansen, Christian Henriksen, Henrik Laurberg Pedersen, Carsten Lunde Petersen^*

^*Corresponding author for this work

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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.

Original language	English
Journal	Potential Analysis
Volume	50
Issue number	3
Pages (from-to)	401-413
ISSN	0926-2601
DOIs	https://doi.org/10.1007/s11118-018-9687-5
Publication status	Published - 2018

Keywords

Orthogonal polynomier
Green’s funktion
Julia mængde
Orthogonal Polynomials
Green's function
Julia set

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10.1007/s11118-018-9687-5

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title = "Julia Sets of Orthogonal Polynomials",

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.",

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AU - Christiansen, Jacob Stordal

AU - Henriksen, Christian

AU - Pedersen, Henrik Laurberg

AU - Petersen, Carsten Lunde

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

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

SN - 0926-2601

VL - 50

SP - 401

EP - 413

JO - Potential Analysis

JF - Potential Analysis

IS - 3

ER -

Julia Sets of Orthogonal Polynomials

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Keywords

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