Generic properties of eigenvalues of the fractional Laplacian

We consider the Dirichlet eigenvalues of the fractional Laplacian, related to a smooth bounded domain. We prove that there exists an arbitrarily small perturbation of the original domain such that all Dirichlet eigenvalues of the fractional Laplacian are simple. As a consequence we obtain that all Dirichlet eigenvalues of the fractional Laplacian on an interval are simple. In addition, we prove that for a generic choice of parameters all the eigenvalues of some non-local operators are also simple.