Extremal polynomials on a Jordan arc

2021/08/04 by Alpan, Gökalp
#33C45 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 41A17 #Secondary 41A44

paper · doi:10.48550/arxiv.2108.01798

Abstract

Let Γ be a C²⁺ Jordan arc and let Γ₀ be the open arc which consists of interior points of Γ. We find concrete upper and lower bounds for the limit of Widom factors for L₂(μ) extremal polynomials on Γ which was given in [18]. In addition, we show that the upper bound for the limit supremum of Widom factors for the weighted Chebyshev polynomials which was obtained in [18] can be improved once two normal derivatives of the Green function do not agree at one point z∈ Γ₀. We also show that if Γ₀ is not analytic then we have improved upper bounds.

Related

• Extremal polynomials and polynomial preimages
• On the Widom factors for L_p extremal polynomials
• On a conjecture of Widom
• Szegő's theorem for Jordan arcs
• Szego\H o-Widom asymptotics of Chebyshev Polynomials on Circular Arcs