R\'esolution du $\partial\bar{\partial}$ pour les courants prolongeables d\'efinis sur un domaine pseudoconvexe non born\'e de $\mathbb{C}^n$

TL;DR

This paper addresses solving the $ar{ar{ ext{d}}}$-equation for extendable currents within unbounded pseudoconvex domains in complex n-space, advancing the understanding of complex analysis in such settings.

Contribution

It provides a solution to the $ar{ar{ ext{d}}}$-equation for extendable currents in unbounded pseudoconvex domains, a problem not previously fully addressed.

Findings

Solved the $ar{ar{ ext{d}}}$-equation for extendable currents

Extended the theory to unbounded pseudoconvex domains

Contributed to complex analysis in non-compact settings

Abstract

In this present paper, we solve the $\partial\bar{\partial}$ for extendable currents definite in a pseudoconvexe unbounded domain of $\mathbb{C}^n$ .