On the asymptotic behavior of \(L_{p}\) extremal polynomials

Abstract

Let \(\beta \) denote a positive Szeg? measure on the unit circle \(\Gamma \) and \(\delta _{z_{k}}\) denote an anatomic measure (\(\delta \) Dirac) centered on the point \(z_{k}.\) We study, for all \(p>0,\) the asymptotic behavior of \(L_{p}\) extremal polynomials with respect to a measure of the type \[ \alpha =\beta +\sum_{k=1}^{\infty }A_{k}\delta _{z_{k}}, \] where \(\left\{ z_{k}\right\} _{k=1}^{\infty }\) is an infinite collection of points outside \(\Gamma \).

Keywords

• asymptotic behavior
• \( L_{p}\) extremal polynomials