Fractional Laplacian, homogeneous Sobolev spaces and their realizations
Classical Analysis and ODEs
2019-12-04 v2
Abstract
We study the fractional Laplacian and the homogeneous Sobolev spaces on R^d , by considering two definitions that are both considered classical. We compare these different definitions, and show how they are related by providing an explicit correspondence between these two spaces, and show that they admit the same representation. Along the way we also prove some properties of the fractional Laplacian.
Keywords
Cite
@article{arxiv.1910.05980,
title = {Fractional Laplacian, homogeneous Sobolev spaces and their realizations},
author = {Alessandro Monguzzi and Marco M. Peloso and Maura Salvatori},
journal= {arXiv preprint arXiv:1910.05980},
year = {2019}
}
Comments
17 pages - some new references and comments have been added