A note on partial polynomial functions, in memory of Marek Jarnicki

TL;DR

This paper discusses an extension theorem for separately holomorphic functions that are polynomial or rational in some variables, contributing to complex analysis and function theory.

Contribution

It introduces a new extension theorem for functions with partial polynomial or rational dependence, advancing understanding in several complex variables.

Findings

Extension theorem for separately holomorphic functions

Applicable to polynomial and rational functions in some variables

Enhances methods for extending functions in complex analysis

Abstract

We present an extension theorem for a separately holomorphic function which is polynomial/rational in some variables.