Analytic continuation of residue currents

TL;DR

This paper proves that the iterated Mellin transform of residue integrals related to complete intersection holomorphic mappings on complex manifolds can be analytically continued near the origin in complex space.

Contribution

It establishes the analytic continuation of the iterated Mellin transform of residue integrals for complete intersection holomorphic mappings.

Findings

Mellin transform of residue integrals can be extended analytically near the origin

The result applies to complex manifolds with complete intersection mappings

Provides a new tool for analyzing residue currents in complex geometry

Abstract

Let $X$ be a complex manifold and $f\colon X\to \C^p$ a holomorphic mapping defining a complete intersection. We prove that the iterated Mellin transform of the residue integral associated to $f$ has an analytic continuation to a neighborhood of the origin in $\C^p$.