On Limits of Sequences of Holomorphic Functions

TL;DR

This paper investigates the behavior of pointwise limits of holomorphic functions in one and several complex variables, offering new insights, results, and exploring uncharted areas in the theory and solutions of elliptic equations.

Contribution

It introduces new perspectives and results on limits of holomorphic functions in multiple variables and extends classical results with novel approaches.

Findings

New results on solutions of elliptic equations

Exploration of limits of holomorphic functions in several variables

Novel viewpoints on classical complex analysis topics

Abstract

We study functions which are the pointwise limit of a sequence of holomorphic functions. In one complex variable this is a classical topic, though we offer some new points of view and new results. Some novel results for solutions of elliptic equations will be treated. In several complex variables the question seems to be new, and we explore some new avenues.