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PreprintCC BY 4.0arXiv

Hankel, Toeplitz, Hermitian--Toeplitz Determinants and the Zalcman Functional for a Class of Biholomorphic Mappings on Complex Banach Spaces

  • Nabadwip Sarkar
  • Pradip Das
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Abstract

In this paper, we investigate the second Hankel determinant, Toeplitz determinants, Hermitian--Toeplitz determinants and the generalized Zalcman functional for a class of normalized biholomorphic mappings on complex Banach spaces. Motivated by recent results for the corresponding class of analytic functions in the unit disk, we establish Banach space analogues of these determinant estimates. Our results extend the one-variable inequalities of Allu, Lecko and Thomas \cite{ALT2022} to the setting of complex Banach spaces, thereby providing higher-dimensional counterparts for the class corresponding to ℱO(λ).

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Cite

BibTeXRIS
BibTeX
@misc{sarkar2026hankel,
  title = {{Hankel, Toeplitz, Hermitian--Toeplitz Determinants and the Zalcman Functional for a Class of Biholomorphic Mappings on Complex Banach Spaces}},
  author = {Nabadwip Sarkar and Pradip Das},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.12511},
  eprint = {2607.12511},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.12511},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Hankel, Toeplitz, Hermitian--Toeplitz Determinants and the Zalcman Functional for a Class of Biholomorphic Mappings on Complex Banach Spaces
AU  - Nabadwip Sarkar
AU  - Pradip Das
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2607.12511
UR  - https://arxiv.org/abs/2607.12511
AB  - In this paper, we investigate the second Hankel determinant, Toeplitz determinants, Hermitian--Toeplitz determinants and the generalized Zalcman functional for a class of normalized biholomorphic mappings on complex Banach spaces. Motivated by recent results for the corresponding class of analytic functions in the unit disk, we establish Banach space analogues of these determinant estimates. Our results extend the one-variable inequalities of Allu, Lecko and Thomas \cite{ALT2022} to the setting of complex Banach spaces, thereby providing higher-dimensional counterparts for the class corresponding to ℱ_O(λ).
ER  -