  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.
