Hodge de Rham theory and analytic torsion for spaces with horn type singularities

We study the global analytic properties of a space $X$ with a horn type singularity. In particular, we introduce some de Rham complex of square integrable forms and we describe its homology and the spectral properties of the associated Hodge Laplace operator. All this is applied to produce a suitable description of the analytic torsion of $X$ and to prove an extension of the Cheeger M\"{u}ller theorem.