Norms of Chebyshev and Faber polynomials on curves with corners and cusps

Erwin Miña-Díaz, Olof Rubin, Aron Wennman

We prove that the $n$th Chebyshev polynomial $T_n$ of a piecewise Dini-smooth Jordan curve $\Gamma$ satisfies \[ \lim_{n\to\infty}\frac{\|T_{n}\|_Γ}{\mathrm{cap}(Γ)^n}=1, \] where $\|…