The Generalized Toeplitz Determinants for a Class of Holomorphic Mappings in Several Complex Variables

Abstract

In this paper, we define the generalized Toeplitz determinants whose entries are the coefficients of holomorphic functions on the unit disk \(\mathbb {U}\) with k-fold symmetric, and then we establish the sharp bounds of the generalized determinants formed over the related terms of homogeneous expansion of a class of holomorphic mappings defined on the unit ball of a complex Banach space. The results presented here would generalize the corresponding results given by Giri and Kumar (Complex Anal Oper Theory 17(6):86, 2023).