Julia Sets of Orthogonal Polynomials

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

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Julia Sets of Orthogonal Polynomials. / Christiansen, Jacob Stordal; Henriksen, Christian; Pedersen, Henrik Laurberg; Petersen, Carsten Lunde.

In: Potential Analysis, Vol. 50, No. 3, 2019, p. 401-413.

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

Harvard

Christiansen, JS, Henriksen, C, Pedersen, HL & Petersen, CL 2019, 'Julia Sets of Orthogonal Polynomials', Potential Analysis, vol. 50, no. 3, pp. 401-413. https://doi.org/10.1007/s11118-018-9687-5

APA

Christiansen, J. S., Henriksen, C., Pedersen, H. L., & Petersen, C. L. (2019). Julia Sets of Orthogonal Polynomials. Potential Analysis, 50(3), 401-413. https://doi.org/10.1007/s11118-018-9687-5

Vancouver

Christiansen JS, Henriksen C, Pedersen HL, Petersen CL. Julia Sets of Orthogonal Polynomials. Potential Analysis. 2019;50(3):401-413. https://doi.org/10.1007/s11118-018-9687-5

Author

Christiansen, Jacob Stordal ; Henriksen, Christian ; Pedersen, Henrik Laurberg ; Petersen, Carsten Lunde. / Julia Sets of Orthogonal Polynomials. In: Potential Analysis. 2019 ; Vol. 50, No. 3. pp. 401-413.

Bibtex

@article{3e8d7822aa134424820c4212a94b85fa,
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 = "Green{\textquoteright}s function, Julia set, Orthogonal polynomials",
author = "Christiansen, {Jacob Stordal} and Christian Henriksen and Pedersen, {Henrik Laurberg} and Petersen, {Carsten Lunde}",
year = "2019",
doi = "10.1007/s11118-018-9687-5",
language = "English",
volume = "50",
pages = "401--413",
journal = "Potential Analysis",
issn = "0926-2601",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - Julia Sets of Orthogonal Polynomials

AU - Christiansen, Jacob Stordal

AU - 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 - Green’s function

KW - Julia set

KW - Orthogonal polynomials

UR - http://www.scopus.com/inward/record.url?scp=85063269345&partnerID=8YFLogxK

U2 - 10.1007/s11118-018-9687-5

DO - 10.1007/s11118-018-9687-5

M3 - Journal article

AN - SCOPUS:85063269345

VL - 50

SP - 401

EP - 413

JO - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

IS - 3

ER -

ID: 222973297