TOEPLITZ DETERMINANTS IN ONE AND HIGHER DIMENSIONS*

doi:10.1007/s10473-024-0517-0

Abstract

Abstract: 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.

Key words: holomorphic mappings, starlike mappings, Toeplitz determinants, coefficient inequalities

CLC Number:

32H02

Surya Giri, S. Sivaprasad Kumar. TOEPLITZ DETERMINANTS IN ONE AND HIGHER DIMENSIONS^*[J].Acta mathematica scientia,Series B, 2024, 44(5): 1931-1944.

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TOEPLITZ DETERMINANTS IN ONE AND HIGHER DIMENSIONS^*

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