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. 
Louis Boutet De Monvel (IMJ), Yves Colin De Verdi\`ere (IF)
math-ph math.AP math.MP