İstanbul Analysis Seminars

Internal Polya inequality in several variables
Vyacheslav P. Zakharyuta
Sabancı University, Turkey
Özet : Suppose $f$ is a function analytic in a domain $\overline{\mathbb{C}} \smallsetminus K$, where $K\subset \mathbb{C}$ is a polynomially convex compact set, with Taylor expansion $f\left( z\right) =\sum_{k=0}^{\infty } \frac{a_{k}}{z^{k+1}}$ at $\infty $, and $H_{s}\left( f\right) :=\det \left( a_{k+l}\right) _{k,l=0}^{s}$ are related Hankel determinants. The classical Polya theorem (1929) says that \[ D\left( f\right) :=\limsup_{s\rightarrow \infty }\left\vert H_{s}\left( f\right) \right\vert ^{1/s^{2}}\leq d\left( K\right) , \] where $d\left( K\right) $ is the transfinite diameter of $K$ introduced by Fekete in 1923. In our talk will be considered some multivariate internal analogs of this result. They are based on the generalized Polya inequality for compacta and on the notion of internal transfinite diameter $d\left( a,\partial D\right) $ of the boundary of a domain $D\subset \mathbb{C}^{n}$ viewed from a given point $a\in D$. The presented results are joint with Ozan Günyüz.
  Tarih : 13.11.2015
  Saat : 15:40
  Yer : Sabancı University, Karaköy Communication Center, Bankalar Caddesi 2, Karaköy
  Dil : English