Fractional Laplacians and Nilpotent Lie Groups

TL;DR

This paper extends the theory of fractional Laplacians to Nilpotent Lie Groups and explores their connection with PDE solutions, offering new perspectives inspired by prior foundational works.

Contribution

It introduces a generalization of fractional Laplacians to Nilpotent Lie Groups, providing novel insights into their properties and associated PDE solutions.

Findings

Fractional Laplacians are extended to Nilpotent Lie Groups.

New relationships between fractional Laplacians and PDE solutions are established.

The work offers a different viewpoint inspired by Caffarelli & Silvestre and Stinga & Torrea.

Abstract

The aim of this short article is to generalize, with a slighthly different point of view, some new results concerning the fractional powers of the Laplace operator to the setting of Nilpotent Lie Groups and to study its relationship with the solutions of a partial differential equation in the spirit of the articles of Caffarelli & Silvestre and Stinga & Torrea.