In this study, we derive the sharp bounds of certain Toeplitz determinants whose entries are the coefficients of holomorphic functions belonging to a class defined on the unit disk $\mathbb{U}$. Furthermore, these results are extended to a class of holomorphic functions on the unit ball in a complex Banach space and on the unit polydisc in $\mathbb{C}^n$. The obtained results provide the bounds of Toeplitz determinants in higher dimensions for various subclasses of normalized univalent functions.
Surya Giri
,
S. Sivaprasad Kumar
. TOEPLITZ DETERMINANTS IN ONE AND HIGHER DIMENSIONS*[J]. Acta mathematica scientia, Series B, 2024
, 44(5)
: 1931
-1944
.
DOI: 10.1007/s10473-024-0517-0
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