Localization of Forelli's theorem

TL;DR

This paper extends Forelli's theorem by localizing it for functions holomorphic along a specific geometric structure called a standard suspension of linear discs, broadening its applicability.

Contribution

It generalizes previous results by providing a localized version of Forelli's theorem for a new class of functions and geometric configurations.

Findings

Established a localization of Forelli's theorem for functions holomorphic along a standard suspension of linear discs.

Extended the original theorem to a broader geometric context.

Generalized prior results, enhancing the theorem's scope.

Abstract

The main purpose of this article is to present a localization of Forelli's theorem for the functions holomorphic along a standard suspension of linear discs. This generalizes one of the main results of \cite{CK21} and the original Forelli's theorem.