Work

A Fractional Laplacian and Its Extension Problem

Year: 2025

Type: article

Abstract: ABSTRACT In this paper, we establish four equivalent characterizations of the fractional Laplacian operator with , in some class of functions on . Here, denotes the Dunkl differential‐difference Laplacian and is a multiplicity function for the Dunkl operators. Starting from the natural Fourier characterization of , we prove Bochner's and singular integral characterizations of . A large part of the paper is dedicated to the fourth characterization where we obtain the fractional Laplacian as a Dirichlet‐to‐Neumann map via an extension problem to the upper half‐plane. We also get a Poisson formula for the extension.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.10846

Authors: Salem Ben Said, Selma Negzaoui

Institutions: United Arab Emirates University, Tunis El Manar University

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $5,000

Funder: United Arab Emirates University