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Toeplitz determinants for starlike mappings of order α in several complex variables
Abstract
Let F(z)=zf(z), where f is a normalized scalar holomorphic function on the unit ball 𝔹 of a complex Banach space X or on the unit polydisk 𝕌n of ℂn. We establish sharp bounds for two Toeplitz determinants involving the second, third and fourth Fréchet derivatives of F when F is starlike of order α, 0≤α<1. The first bound is sharp for the full range 0≤α<1, while the second is sharp for 0≤α≤ 2/3. The extremal mappings are explicitly identified, confirming the sharpness of the estimates.
Related
- Hankel, Toeplitz, Hermitian--Toeplitz Determinants and the Zalcman Functional for a Class of Biholomorphic Mappings on Complex Banach Spaces
- The Fekete-Szegö problem for starlike mappings of order α and quasi-convex mappings of type B in the unit balls of complex Banach spaces
- Sharp Robertson-type coefficient estimates for radial starlike and quasi-convex of type B mappings of order α in complex Banach spaces
- Estimates for a Parameterized Hankel Functional of Starlike Mappings of Order α and Quasi-Convex Mappings of Type B in Complex Banach Spaces
- On coefficient theorems for starlike and quasi-convex of type B mappings in complex Banach spaces
BibTeX
@misc{panja2026toeplitz,
title = {{Toeplitz determinants for starlike mappings of order α in several complex variables}},
author = {Shantanu Panja and Sujoy Majumder and Abhijit Banerjee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15497},
eprint = {2610.15497},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15497},
}
RIS
TY - UNPB
TI - Toeplitz determinants for starlike mappings of order α in several complex variables
AU - Shantanu Panja
AU - Sujoy Majumder
AU - Abhijit Banerjee
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15497
UR - https://arxiv.org/abs/2610.15497
AB - Let F(z)=zf(z), where f is a normalized scalar holomorphic function on the unit ball 𝔹 of a complex Banach space X or on the unit polydisk 𝕌^n of ℂ^n. We establish sharp bounds for two Toeplitz determinants involving the second, third and fourth Fréchet derivatives of F when F is starlike of order α, 0≤α<1. The first bound is sharp for the full range 0≤α<1, while the second is sharp for 0≤α≤ 2/3. The extremal mappings are explicitly identified, confirming the sharpness of the estimates.
ER -