Julia Sets of Orthogonal Polynomials
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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
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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