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.