# Widom factors for the Hilbert norm

Gökalp Alpan; Alexander Goncharov

Banach Center Publications (2015)

- Volume: 107, Issue: 1, page 11-18
- ISSN: 0137-6934

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topGökalp 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 -

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