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.

Kategorie tematyczne

• 30C85: Capacity and harmonic measure in the complex plane
• 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
• 42C05: Orthogonal functions and polynomials, general theory
• 47B36: Jacobi (tridiagonal) operators (matrices) and generalizations

• 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