Symmetrization of Suffridge polynomials and approximation of T-symmetric Koebe functions

Dmitriy Dmitrishin; Andrey Smorodin; Alex Stokolos; Mihai Tohaneanu

doi:10.1016/j.jmaa.2021.125350

Symmetrization of Suffridge polynomials and approximation of T-symmetric Koebe functions

Dmitriy Dmitrishin, Andrey Smorodin, Alex Stokolos, Mihai Tohaneanu

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The article studies extremal properties of certain T-symmetric polynomials, which generalize the famous Suffridge polynomials. Our first result establishes an asymptotic estimate for the maximum modulus in the unit disk. Our second result uses these polynomials to approximate univalent functions in the unit disk, which is the analogue of the Andrievskii-Ruscheweych subordination [1] to T-symmetric polynomials. The main technical tool is a limit formula for representing an exponential function as a product of trigonometric functions.

Original language	English
Article number	125350
Journal	Journal of Mathematical Analysis and Applications
Volume	503
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2021.125350
State	Published - Nov 15 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.

Funding

M.T. is partially supported by a grant from the Simons Foundation (# 586051 ).

Funders	Funder number
Simons Foundation	586051

Keywords

Suffridge polynomials
T-symmetric Koebe function
T-symmetric univalent polynomials

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2021.125350

Cite this

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abstract = "The article studies extremal properties of certain T-symmetric polynomials, which generalize the famous Suffridge polynomials. Our first result establishes an asymptotic estimate for the maximum modulus in the unit disk. Our second result uses these polynomials to approximate univalent functions in the unit disk, which is the analogue of the Andrievskii-Ruscheweych subordination [1] to T-symmetric polynomials. The main technical tool is a limit formula for representing an exponential function as a product of trigonometric functions.",

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AU - Smorodin, Andrey

AU - Stokolos, Alex

AU - Tohaneanu, Mihai

PY - 2021/11/15

Y1 - 2021/11/15

N2 - The article studies extremal properties of certain T-symmetric polynomials, which generalize the famous Suffridge polynomials. Our first result establishes an asymptotic estimate for the maximum modulus in the unit disk. Our second result uses these polynomials to approximate univalent functions in the unit disk, which is the analogue of the Andrievskii-Ruscheweych subordination [1] to T-symmetric polynomials. The main technical tool is a limit formula for representing an exponential function as a product of trigonometric functions.

AB - The article studies extremal properties of certain T-symmetric polynomials, which generalize the famous Suffridge polynomials. Our first result establishes an asymptotic estimate for the maximum modulus in the unit disk. Our second result uses these polynomials to approximate univalent functions in the unit disk, which is the analogue of the Andrievskii-Ruscheweych subordination [1] to T-symmetric polynomials. The main technical tool is a limit formula for representing an exponential function as a product of trigonometric functions.

KW - Suffridge polynomials

KW - T-symmetric Koebe function

KW - T-symmetric univalent polynomials

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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Symmetrization of Suffridge polynomials and approximation of T-symmetric Koebe functions

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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