Multidimensional analogs of the Fekete--Szegö functional

2024/06/04 by Mark Elin, Elin, Mark, Fiana Jacobzon +1
Chemistry · #Chemical Thermodynamics and Molecular Structure #Complex Variables (math.CV) #FOS: Mathematics #Molecular spectroscopy and chirality #Radioactive element chemistry and processing

paper · pdf · doi:10.48550/arxiv.2406.02752

openalex publication_date 2024/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 studied modifications of the Fekete--Szegö functional are either special cases or `components' of the mapping we introduce. The study involves the examination of transforms of the Fekete--Szegö mapping under specific transformations applied to given holomorphic mappings. We show that for a mapping f, the third order Fréshet derivative of the inverse mapping f^-1 and of elements of the semigroup generated by f can be expressed in terms of the Fekete--Szegö mapping. Estimates of the Fekete--Szegö mapping over some subclasses of semigroup generators and of starlike mappings are also presented.

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