Conformally Invariant Non-local Operators

On a conformal manifold with boundary, we construct conformally invariant local boundary conditions B for the conformally invariant power of the Laplacian k , with the property that ( k , B) is formally self-adjoint. These boundary problems are used to construct conformally invariant nonlocal operators on the boundary Σ, generalizing the conformal Dirichlet-to-Robin operator, with principal parts which are odd powers h (not necessarily positive) of (−∆Σ)1/2, where ∆Σ is the boundary Laplace operator. The constructions use tools from a conformally invariant calculus.