Some Results of Fekete-Szegö Type. Results for Some Holomorphic Functions of Several Complex Variables - Długosz, Renata; Liczberski, Piotr (Symmetry (Basel), 2020)
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.