695 research outputs found
The action of pseudo-differential operators on functions harmonic outside a smooth hyper-surface
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
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