Some Results of Fekete-Szegö Type. Results for Some Holomorphic Functions of Several Complex Variables

This paper is devoted to a generalization of the well-known Fekete-Szegö type coefficients problem for holomorphic functions of a complex variable onto holomorphic functions of several variables. The considerations concern three families of such functions f, which are bounded, having positive real p...

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Vydané v:Symmetry (Basel) Ročník 12; číslo 10; s. 1707
Hlavní autori: Długosz, Renata, Liczberski, Piotr
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel MDPI AG 01.10.2020
Predmet:
Analytic functions
Complex variables
Estimates
Inequality
Mathematical analysis
Polynomials
Power series
Series expansion
ISSN:2073-8994, 2073-8994
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Abstract This paper is devoted to a generalization of the well-known Fekete-Szegö type coefficients problem for holomorphic functions of a complex variable onto holomorphic functions of several variables. The considerations concern three families of such functions f, which are bounded, having positive real part and which Temljakov transform Lf has positive real part, respectively. The main result arise some sharp estimates of the Minkowski balance of a combination of 2-homogeneous and the square of 1-homogeneous polynomials occurred in power series expansion of functions from aforementioned families.
AbstractList This paper is devoted to a generalization of the well-known Fekete-Szegö type coefficients problem for holomorphic functions of a complex variable onto holomorphic functions of several variables. The considerations concern three families of such functions f, which are bounded, having positive real part and which Temljakov transform Lf has positive real part, respectively. The main result arise some sharp estimates of the Minkowski balance of a combination of 2-homogeneous and the square of 1-homogeneous polynomials occurred in power series expansion of functions from aforementioned families.
Author Liczberski, Piotr
Długosz, Renata
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Cites_doi 10.1080/17476933.2013.794139
10.1201/9781482289817
10.1201/9780203911624
10.1090/S0002-9939-1969-0232926-9
10.1112/jlms/s1-8.2.85
ContentType Journal Article
Copyright 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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SubjectTerms Analytic functions
Complex variables
Estimates
Inequality
Mathematical analysis
Polynomials
Power series
Series expansion
Title Some Results of Fekete-Szegö Type. Results for Some Holomorphic Functions of Several Complex Variables
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