What question did this study set out to answer?

The aim is to generalize the Graham–Kohr extension operator and explore its relationships within Loewner chains.

April 10, 2026Open Access

A Generalized Graham–Kohr Extension Operator and Loewner Chains in the Unit Ball

Key Points

The aim is to generalize the Graham–Kohr extension operator and explore its relationships within Loewner chains.
Studied the Graham–Kohr extension operator Ψn,α,βγ(f) for functions on the unit disk.
Applied the theory of Loewner chains to investigate geometric properties.
Established subordination relations for starlike functions under specific parameter choices.
Showed that the extension operator can be embedded in a Loewner chain.
Preserved critical geometric properties in the embedding.
Found new subordination relations among starlike functions based on parameter selection.

Abstract

In this paper, we study a generalization of the Graham–Kohr extension operator, Ψn,α,βγ(f), which maps functions defined on the unit disk into holomorphic mappings in the unit ball Bn. Using the theory of Loewner chains, we show that, under suitable conditions, this operator can be embedded as the first element of a Loewner chain while preserving geometric properties. In addition, for suitable choices of the parameters, we establish subordination relations among starlike functions.

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Authors

Anamaria Paștiu

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Mathematics

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Babeș-Bolyai University

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A Generalized Graham–Kohr Extension Operator and Loewner Chains in the Unit Ball

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Abstract

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