1209.5165 (Louis Boutet De Monvel et al.)

The action of pseudo-differential operators on functions harmonic
outside a smooth hyper-surface    [PDF]

Louis Boutet De Monvel, Yves Colin De Verdière

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.

View original: http://arxiv.org/abs/1209.5165