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

Producción científica: Article › revisión exhaustiva

5 Citas (Scopus)

Resumen

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.

Idioma original	English
Número de artículo	125350
Publicación	Journal of Mathematical Analysis and Applications
Volumen	503
N.º	2
DOI	https://doi.org/10.1016/j.jmaa.2021.125350
Estado	Published - nov 15 2021

Nota bibliográfica

Publisher Copyright:
© 2021 Elsevier Inc.

Financiación

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

Financiadores	Número del financiador
Simons Foundation	586051

ASJC Scopus subject areas

Analysis
Applied Mathematics

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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 - Dmitrishin, Dmitriy

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

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ASJC Scopus subject areas

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