Operational calculus for holonomic distributions in the framework of D-module theory

TL;DR

This paper develops an algorithmic approach within D-module theory to analyze the distribution $f_+^a7$ with a meromorphic parameter, focusing on its Laurent expansion and integration, for holonomic distributions.

Contribution

It introduces a novel algorithmic framework for studying parameter-dependent distributions in D-module theory, specifically addressing their Laurent expansions and integrability.

Findings

Provides a method to compute Laurent expansions of holonomic distributions.

Establishes a framework for analyzing distributions with a meromorphic parameter.

Enhances understanding of distributions satisfying holonomic systems of differential equations.

Abstract

Let $f$ be a real polynomial of $x = (x_1,\dots,x_n)$ and $\varphi$ be a locally integrable function of $x$ which satisfies a holonomic system of linear differential equations. We study the distribution $f_+^\lambda\varphi$ with a meromorphic parameter $\lambda$, especially its Laurent expansion and integration, from an algorithmic viewpoint in the framework of $D$-module theory.