Toeplitz determinants on bounded starlike circular domain in $\mathbb{C}^n$

TL;DR

This paper establishes sharp bounds for Toeplitz determinants associated with holomorphic mappings on bounded starlike circular domains in higher-dimensional complex spaces, extending classical results from the unit disk to multiple dimensions.

Contribution

It extends known bounds for Toeplitz determinants from the unit disk to higher-dimensional starlike circular domains in complex space.

Findings

Derived sharp bounds for Toeplitz determinants in higher dimensions.

Extended classical bounds from one-dimensional to multi-dimensional settings.

Applicable to subclasses of normalized analytic univalent functions.

Abstract

In this paper, we derive the sharp bounds of Toeplitz determinants for a class of holomorphic mappings on the bounded starlike circular domain $\Omega$ in $\mathbb{C}^n$, which extend certain known bounds for various subclasses of normalized analytic univalent functions in the unit disk to higher dimensions.