15 papers
On one filtration of holomorphic functions
Fiana Jacobzon
In this work we consider a family of function classes constructed by means of the Gauss hypergeometric function . We demonstrate that this fam…
Nonlinear resolvents in the unit disk: geometry and dynamics
Mark Elin, Fiana Jacobzon
In this paper we present a unified approach to the study of geometric and dynamic properties of nonlinear resolvents of holomorphic generators. The idea is to apply the distortion…
Multidimensional analogs of the Fekete--Szegö functional
Mark Elin, Fiana Jacobzon
In this paper we introduce the Fekete--Szegö type mapping in the open unit ball of a complex Banach space. % and study its geometric and analytical properties. All previously studi…
On the hypergeometric function and families of holomorphic functions
Mark Elin, Fiana Jacobzon
In this work, we examine one two-parameter family of sets consisting of functions holomorphic in the unit disk, previously investigated by several mathematicians. We focus on the s…
Survey on filtrations (parametric embeddings) of infinitesimal generators
Mark Elin, Fiana Jacobzon
This work is devoted to the so-called filtration theory of semigroup generators in the unit disk. It should be noted that numerous filtrations studied to nowdays have been introduc…
The Fekete--Szegö problem for spirallike mappings and non-linear resolvents in Banach spaces
Mark Elin, Fiana Jacobzon
We study the Fekete--Szegö problem on the open unit ball of a complex Banach space. Namely, the Fekete--Szegö inequalities are proved for the class of spirallike mappings relative…