English

An extension theorem for some pseudo-differential operators

Analysis of PDEs 2012-05-25 v2

Abstract

In this paper we provide an extension theorem for fractional powers of some pseudo-differential operators P(D)P(D). These extensions yields realization of the fractional powers of some pseudo-differential operators in the spirit of Caffarelli and Silvestre \cite{CSilv}. In particular every fractional power of a local pseudo-differential operator can be realized locally. We also give some properties of the relativistic Schr\"odinger operator \Dsm\Dsm.

Keywords

Cite

@article{arxiv.1205.4320,
  title  = {An extension theorem for some pseudo-differential operators},
  author = {Mouhamed Moustapha Fall},
  journal= {arXiv preprint arXiv:1205.4320},
  year   = {2012}
}

Comments

This paper has been withdrawn because the main result has been already proved. The remaining part of the paper will appear in a forthcoming one

R2 v1 2026-06-21T21:06:38.300Z