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

Department of Mathematical Sciences

3 Citations (Scopus)

13 Downloads (Pure)

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
Journal	Potential Analysis
Volume	50
Issue number	3
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

Keywords

Green’s function
Julia set
Orthogonal polynomials

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10.1007/s11118-018-9687-5

OAversion-Julia Sets of Orthogonal PolynomialsAccepted author manuscript, 9.88 MB

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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.

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KW - Julia set

KW - Orthogonal polynomials

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DO - 10.1007/s11118-018-9687-5

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Julia Sets of Orthogonal Polynomials

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Keywords

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