An extension theorem for some pseudo-differential operators

2012/05/19 by Mouhamed Moustapha Fall, Fall, Mouhamed Moustapha
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1205.4320

This paper has been withdrawn because the main result has been already proved.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

arxiv created 2012/05/24 · arxiv updated 2012/05/25

Abstract

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

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