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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Bibliographic Details
Published in:Symmetry (Basel) Vol. 12; no. 10; p. 1707
Main Authors: Długosz, Renata, Liczberski, Piotr
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.10.2020
Subjects:
Analytic functions
Complex variables
Estimates
Inequality
Mathematical analysis
Polynomials
Power series
Series expansion
ISSN:2073-8994, 2073-8994
Online Access:Get full text
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Summary: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.
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ISSN:2073-8994
2073-8994
DOI:10.3390/sym12101707