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

Bidragets oversatte titel: Juliamængder for orthogonale polynomier

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

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

Abstract

For et sandsynlighedsmål med kompakt ikke-polær støtte i den komplekse plan relaterer vi de dynamiske egenskaber ved den associerede følge af orthonormale polynomier {P n} til egenskaberne for støtten. Mere præcist relaterer vi Julia mængden for P_n til den ydre rand af støtten, den udfyldte Juliamængde til den udfyldte støtte og Green's funktion for P_n med Green's funktionen for komplementet til den udfyldte støtte.

Bidragets oversatte titel	Juliamængder for orthogonale polynomier
Originalsprog	Engelsk
Tidsskrift	Potential Analysis
Vol/bind	50
Sider (fra-til)	401-413
Antal sider	13
ISSN	0926-2601
DOI	https://doi.org/10.1007/s11118-018-9687-5
Status	Udgivet - 2019

Bibliografisk 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”.

Emneord

Orthogonal polynomier
Green’s funktion
Julia mængde

Link til dokument

10.1007/s11118-018-9687-5

orthogonalAccepteret manuskript, 16,3 MBLicens: Ikke-specificeret

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

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

Citer dette

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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",

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journal = "Potential Analysis",

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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

SN - 0926-2601

VL - 50

SP - 401

EP - 413

JO - Potential Analysis

JF - Potential Analysis

ER -

Julia Sets of Orthogonal Polynomials

Abstract

Bibliografisk note

Emneord

Link til dokument

Projekter

Holomorpic Dynamics and Orthogonal Polynomials

Citer dette