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 tidsskriftTidsskriftartikelForskningpeer review

Resumé

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.
OriginalsprogEngelsk
TidsskriftPotential Analysis
Antal sider13
ISSN0926-2601
DOI
StatusE-pub ahead of print - 23 feb. 2018

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

Citer dette

Christiansen, Jacob Stordal ; Henriksen, Christian ; Petersen, Henrik Laurberg ; Petersen, Carsten Lunde. / Julia Sets of Orthogonal Polynomials. I: Potential Analysis. 2018.
@article{48872f5a529445d48049f0a0f89c6791,
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’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 = "2018",
month = "2",
day = "23",
doi = "10.1007/s11118-018-9687-5",
language = "English",
journal = "Potential Analysis",
issn = "0926-2601",
publisher = "Springer Netherlands",

}

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

I: Potential Analysis, 23.02.2018.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Julia Sets of Orthogonal Polynomials

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 - 2018/2/23

Y1 - 2018/2/23

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

JO - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

ER -