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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Vydáno v:Symmetry (Basel) Ročník 12; číslo 10; s. 1707
Hlavní autoři: Długosz, Renata, Liczberski, Piotr
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.10.2020
Témata:
Analytic functions
Complex variables
Estimates
Inequality
Mathematical analysis
Polynomials
Power series
Series expansion
ISSN:2073-8994, 2073-8994
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Shrnutí: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