Analytic dilation on complete manifolds with corners of codimension 2

Abstract

The analytic dilation method was originally used in the context of many body Schrödinger operators. In this thesis we adapt it to the context of compatible Laplacians on complete manifolds with corners of codimension two. As in the original setting of application, the method allows us to meromorphically extend the matrix elements associated to analytic vectors; to prove absence of singular spectrum; to find a discrete set that contains the accumulations points of the pure point spectrum; finally, it provides a theory of quantum resonances. Apart from these results, we not only obtain a deeper understanding of the essential spectrum of compatible Laplacians on complete manifolds with corners of codimension 2 but also of the spectral resolution of absolutely continuous states via the definition of generalized eigenfunctions.