Title: Strong asymptotics for Szeg\H{o} polynomials for non-smooth curves
Abstract:
Strong asymptotics for Szeg\H{o} polynomials, i.e., polynomials orthonormal
with respect to the arclength measure on a rectifiable Jordan curve $\Gamma$ in $\mathbb{C}$, have been first
derived in the early 1920's by G. Szeg\H{o}, under the assumption that $\Gamma$ is an analytic Jordan curve.
The transition from analytic to smooth was not obvious and it took almost half a century, in the 1960's,
when P.K. Suetin has been able to derive similar asymptotics for smooth Jordan curves.
The purpose on the talk is to report on some recent results on the strong asymptotics of
Szeg\H{o} polynomials, in cases when $\Gamma$ is a non-smooth Jordan curve,
in particular, piecewise analytic without cusps.