Fourier-Laplace transform and isomonodromic deformations

TL;DR

This paper explores how the Fourier-Laplace transform can be used to describe isomonodromic deformations of meromorphic connections on the Riemann sphere, generalizing previous results to include more complex singularities.

Contribution

It extends the understanding of isomonodromy equations by incorporating both unramified and ramified irregular singularities through Fourier-Laplace transform techniques.

Findings

Generalizes Harnad and Woodhouse's results

Describes isomonodromy equations for broader class of singularities

Provides a unified framework for irregular singularities

Abstract

Using the Fourier-Laplace transform, we describe the isomonodromy equations for meromorphic connections on the Riemann sphere with unramified irregular singularities as those for connections with a (possibly ramified) irregular singularity and a regular singularity. This generalizes some results of Harnad and Woodhouse.