  The present paper provides a new representation of the solution to the
fragmentation equation as a power series in the Banach space of Radon measures
endowed with the total variation norm. This representation is used to justify
how the fragmentation kernel, which is one of the two key parameters of the
fragmentation equation, can be recovered from short-time experimental
measurements of the particle size distributions when the initial condition is a
delta function. A new stability result for this equation is also provided using
a Wasserstein-type norm. We exploit this stability to prove the robustness of
our reconstruction formula with respect to noise and initial data.
