Bieberbach conjecture, Bohr radius, Bloch constant and Alexander's theorem in infinite dimensions

2024/09/06 by Hamada, Hidetaka, Kohr, Gabriela, Kohr, Mirela
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.04028

Abstract

In this paper, we investigate holomorphic mappings F on the unit ball \mathbbB of a complex Banach space of the form F(x)=f(x)x, where f is a holomorphic function on \mathbbB. First, we investigate criteria for univalence, starlikeness and quasi-convexity of type B on \mathbbB. Next, we investigate a generalized Bieberbach conjecture, a covering theorem and a distortion theorem, the Fekete-Szegö inequality, lower bound for the Bloch constant, and Alexander's type theorem for such mappings.

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