Toeplitz Determinants for a Class of Holomorphic Mappings in Higher Dimensions

Abstract

In this paper, we establish the sharp bounds of certain Toeplitz determinants formed over the coefficients of mappings from a class defined on the unit ball of complex Banach space and on the unit polydisc in ${\mathbb{C}}^n$. Derived bounds provide certain new results for the subclasses of normalized univalent functions and extend some known results in higher dimensions.