The action of pseudo-differential operators on functions harmonic outside a smooth hyper-surface
Mathematical Physics
2012-09-27 v1 Analysis of PDEs
math.MP
Abstract
We consider a smooth hyper-surface Z of a closed Riemannian manifold X. Let P be the Poisson operator associating to a smooth function on Z its harmonic extension on X\Z. If A is a pseudo-differential operator on X of degree <3, we prove that B=P^* A P is a pseudo-differential operator on Z and calculate the principal symbol of B.
Cite
@article{arxiv.1209.5165,
title = {The action of pseudo-differential operators on functions harmonic outside a smooth hyper-surface},
author = {Louis Boutet De Monvel and Yves Colin De Verdière},
journal= {arXiv preprint arXiv:1209.5165},
year = {2012}
}