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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-1,
author = {G\"okalp Alpan and Alexander Goncharov},
title = {Widom factors for the Hilbert norm},
journal = {Banach Center Publications},
volume = {104},
year = {2015},
pages = {11-18},
zbl = {06556699},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-1}
}
Gökalp Alpan; Alexander Goncharov. Widom factors for the Hilbert norm. Banach Center Publications, Tome 104 (2015) pp. 11-18. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-1/