Toeplitz determinants for a class of holomorphic mappings in higher dimensions. (English) Zbl 1522.32014
Summary: In this paper, we establish the sharp bounds of certain Toeplitz determinants formed over the coefficients of holomorphic mappings from a class defined on the unit ball of a 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.
MSC:
| 32A30 | Other generalizations of function theory of one complex variable |
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C50 | Coefficient problems for univalent and multivalent functions of one complex variable |
| 32K12 | Holomorphic maps with infinite-dimensional arguments or values |
Keywords:
holomorphic functions on the ball of a complex Banach space; Toeplitz determinants; coefficient inequalitiesReferences:
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