Widom factors for the Hilbert norm

• Autorzy: Gökalp Alpan , Alexander Goncharov
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2015
• Tom: 107
• Numer: 1
• Strony: 11-18

Daty

wydano

2015

Twórcy

autor

Gökalp Alpan

• Department of Mathematics, Bilkent University, 06800, Ankara, Turkey

autor

Alexander Goncharov

• Department of Mathematics, Bilkent University, 06800, Ankara, Turkey

Identyfikatory

DOI

10.4064/bc107-0-1