Cross theorem with singularities - pluripolar vs. analytic case

TL;DR

This paper demonstrates that in the extension of separately holomorphic functions with singularities, the case of analytic singularities can be derived from the pluripolar singularities case, simplifying the understanding of such extensions.

Contribution

It establishes that the extension theorem for functions with analytic singularities follows from the case with pluripolar singularities, unifying these cases.

Findings

Analytic singularities case follows from pluripolar singularities case

Extension theorem applies to separately holomorphic functions with singularities

Simplifies the understanding of singularities in complex analysis

Abstract

We prove that in the extension theorem for separately holomorphic functions on an $N$-fold cross with singularities the case of analytic singularities follows from the case of pluripolar singularities.