Irregular holonomic kernels and Laplace transform

TL;DR

This paper investigates the relationship between irregular holonomic kernels and the Laplace transform using advanced sheaf theory, establishing a commutation property with the De Rham functor for holonomic D-modules.

Contribution

It proves that the correspondence associated with a holonomic D-module commutes with the De Rham functor, extending understanding of Laplace transform in the context of irregular holonomic kernels.

Findings

Established commutation of the correspondence with the De Rham functor

Applied the result to classical Laplace transform analysis

Utilized ind-sheaves and enhanced sheaf theory tools

Abstract

Given a (not necessarily regular) holonomic D-module defined on the product of two complex manifolds, we prove that the associated correspondence commutes (in some sense) with the De Rham functor. We apply this result to the study of the classical Laplace transform. The main tools used here are the theory of ind-sheaves and its enhanced version.