A Liouville theorem for some Bessel generalized operators

TL;DR

This paper proves a Liouville theorem for a broad class of Bessel-related operators in a distribution space, extending classical results and providing two different proofs based on distribution representations.

Contribution

It generalizes the Liouville theorem to a wider class of Bessel-type operators in higher dimensions, with two novel proof techniques.

Findings

Established a Liouville theorem for generalized Bessel operators

Extended classical results to a broader operator class

Provided two distinct proofs using distribution support representations

Abstract

In this paper we establish a Liouville theorem in $\mathcal{H'}_{\mu}$ for a wider class of operators in $(0,\infty)^{n}$ that generalizes the $n$-dimensional Bessel operator. We will present two different proofs, based in two representation theorems for certain distributions "supported in zero".