  Unfolding problems often arise in the context of statistical data analysis.
Such problematics occur when the probability distribution of a physical
quantity is to be measured, but it is randomized (smeared) by some well
understood process, such as a non-ideal detector response or a well described
physical phenomenon. In such case it is said that the original probability
distribution of interest is folded by a known response function. The
reconstruction of the original probability distribution from the measured one
is called unfolding. That technically involves evaluation of the non-bounded
inverse of an integral operator over the space of L^1 functions, which is known
to be an ill-posed problem. For the pertinent regularized operator inversion,
we propose a linear iterative formula and provide proof of convergence in a
probability theory context. Furthermore, we provide formulae for error
estimates at finite iteration stopping order which are of utmost importance in
practical applications: the approximation error, the propagated statistical
error, and the propagated systematic error can be quantified. The arguments are
based on the Riesz-Thorin theorem mapping the original L^1 problem to L^2
space, and subsequent application of ordinary L^2 spectral theory of operators.
A library implementation in C of the algorithm along with corresponding error
propagation is also provided. A numerical example also illustrates the method
in operation.
