Widom factors for the Hilbert norm

Gökalp Alpan, and Alexander Goncharov. "Widom factors for the Hilbert norm." Banach Center Publications 107.1 (2015): 11-18. <http://eudml.org/doc/281797>.

@article{GökalpAlpan2015,
abstract = {Given a probability measure μ with non-polar compact support K, we define the n-th Widom factor W²ₙ(μ) as the ratio of the Hilbert norm of the monic n-th orthogonal polynomial and the n-th power of the logarithmic capacity of K. If μ is regular in the Stahl-Totik sense then the sequence $(W²ₙ(μ))_\{n=0\}^\{∞\}$ has subexponential growth. For measures from the Szegő class on [-1,1] this sequence converges to some proper value. We calculate the corresponding limit for the measure that generates the Jacobi polynomials, analyze the behavior of the corresponding limit as a function of the parameters and review some other examples of measures when Widom factors can be evaluated.},
author = {Gökalp Alpan, Alexander Goncharov},
journal = {Banach Center Publications},
keywords = {orthogonal polynomials; Jacobi weight; Szegö class; Widom condition; Julia sets},
language = {eng},
number = {1},
pages = {11-18},
title = {Widom factors for the Hilbert norm},
url = {http://eudml.org/doc/281797},
volume = {107},
year = {2015},
}

TY - JOUR
AU - Gökalp Alpan
AU - Alexander Goncharov
TI - Widom factors for the Hilbert norm
JO - Banach Center Publications
PY - 2015
VL - 107
IS - 1
SP - 11
EP - 18
AB - Given a probability measure μ with non-polar compact support K, we define the n-th Widom factor W²ₙ(μ) as the ratio of the Hilbert norm of the monic n-th orthogonal polynomial and the n-th power of the logarithmic capacity of K. If μ is regular in the Stahl-Totik sense then the sequence $(W²ₙ(μ))_{n=0}^{∞}$ has subexponential growth. For measures from the Szegő class on [-1,1] this sequence converges to some proper value. We calculate the corresponding limit for the measure that generates the Jacobi polynomials, analyze the behavior of the corresponding limit as a function of the parameters and review some other examples of measures when Widom factors can be evaluated.
LA - eng
KW - orthogonal polynomials; Jacobi weight; Szegö class; Widom condition; Julia sets
UR - http://eudml.org/doc/281797
ER -