An extension theorem for some pseudo-differential operators

Mouhamed Moustapha Fall

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arXiv · 1205.4320

An extension theorem for some pseudo-differential operators

Mouhamed Moustapha Fall

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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 \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 Schrödinger operator $\Dsm$.

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Mouhamed Moustapha Fall. 2012-05-24. An extension theorem for some pseudo-differential operators. https://arxiv.org/abs/1205.4320

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