Julia sets of orthogonal polynomials

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

doi:10.1007/s11118-018-9687-5

Julia sets of orthogonal polynomials

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

Mathematics (Faculty of Engineering)

Research output: Contribution to journal › Article › 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 {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.

Original language	English
Pages (from-to)	401–413
Number of pages	13
Journal	Potential Analysis
Volume	50
Issue number	3
Early online date	2018
DOIs	https://doi.org/10.1007/s11118-018-9687-5
Publication status	Published - 2019

Subject classification (UKÄ)

Mathematical Analysis

Free keywords

Orthogonal polynomials
Julia set
Green’s function

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10.1007/s11118-018-9687-5

Cite this

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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 {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{\textquoteright}s function associated with P n to the Green{\textquoteright}s function for the complement of K.",

keywords = "Orthogonal polynomials, Julia set, Green{\textquoteright}s function",

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

year = "2019",

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language = "English",

volume = "50",

pages = "401–413",

journal = "Potential Analysis",

issn = "1572-929X",

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TY - JOUR

T1 - Julia sets of orthogonal polynomials

AU - Christiansen, Jacob Stordal

AU - Christian Henriksen, Christian

AU - Pedersen, Henrik Laurberg

AU - Petersen, Carsten Lunde

PY - 2019

Y1 - 2019

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 {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.

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 {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.

KW - Orthogonal polynomials

KW - Julia set

KW - Green’s function

U2 - 10.1007/s11118-018-9687-5

DO - 10.1007/s11118-018-9687-5

M3 - Article

SN - 1572-929X

VL - 50

SP - 401

EP - 413

JO - Potential Analysis

JF - Potential Analysis

IS - 3

ER -

Julia sets of orthogonal polynomials

Abstract

Subject classification (UKÄ)

Free keywords

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Cite this