On one filtration of holomorphic functions

2025/12/24 by Fiana Jacobzon, Jacobzon, Fiana
Mathematics · #Analytic and geometric function theory #Holomorphic and Operator Theory #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2512.21405

Abstract

In this work we consider a family of function classes constructed by means of the Gauss hypergeometric function ₂F₁(1,1;2;z) =-(log(1-z))/(z). We demonstrate that this family, in fact, constitutes classes of analytic functions subject to prescribed constraints on their derivatives. For these classes we obtain some geometric characteristics, including sharp coefficient estimates. Moreover, we show that this family naturally provides a filtration of infinitesimal generators, and investigate the corresponding dynamical behavior of the associated semigroups. It is interesting that this filtration links to the Ma--Minda starlike functions.

Citations

• On the hypergeometric function and families of holomorphic functions
• Survey on filtrations (parametric embeddings) of infinitesimal generators
• The Fekete--Szegö problem for spirallike mappings and non-linear resolvents in Banach spaces
• Estimates on some functionals over non-linear resolvents
• Analyticity of semigroups on the right half-plane
• Analyticity and compactness of semigroups of composition operators

Related

• On the hypergeometric function and families of holomorphic functions
• Survey on filtrations (parametric embeddings) of infinitesimal generators
• Geometric properties of the nonlinear resolvent of holomorphic generators
• A Novel Class of Starlike Functions
• Coefficient estimates of certain subclasses of analytic functions associated with Hohlov operator