Toeplitz determinants whose elements are the coefficients of univalent functions

Abstract

Let $\mathcal{S}$ denote the class of analytic and univalent functions in $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1\}$ of the form $f(z)=z+{\sum }_{n=2}^{\infty }{a}_n{z}^n$. In this paper, we determine sharp estimates for the Toeplitz determinants whose elements are the Taylor coefficients of functions in $\mathcal{S}$ and its certain subclasses. We also discuss similar problems for typically real functions.

12 pages