  Hadronic spectral densities are important quantities whose non-perturbative
knowledge allows for calculating phenomenologically relevant observables, such
as inclusive hadronic cross-sections and non-leptonic decay-rates. The
extraction of spectral densities from lattice correlators is a notoriously
difficult problem because lattice simulations are performed in Euclidean time
and lattice data are unavoidably affected by statistical and systematic
uncertainties. In this paper we present a new method for extracting hadronic
spectral densities from lattice correlators. The method allows for choosing a
smearing function at the beginning of the procedure and it provides results for
the spectral densities smeared with this function together with reliable
estimates of the associated uncertainties. The same smearing function can be
used in the analysis of correlators obtained on different volumes, such that
the infinite volume limit can be studied in a consistent way. While the method
is described by using the language of lattice simulations, in reality it is
completely general and can profitably be used to cope with inverse problems
arising in different fields of research.
