Rate of convergence to self-similarity for the fragmentation equation in   L^1 spaces
  In a recent result by the authors (ref. [1]) it was proved that solutions of the self-similar fragmentation equation converge to equilibrium exponentially fast. This was done by showing a spectral gap in weighted $L^2$ spaces of the operator defining the time evolution. In the present work we prove that there is also a spectral gap in weighted $L^1$ spaces, thus extending exponential convergence to a larger set of initial conditions. The main tool is an extension result in ref. [4]. 
Mar\'ia J. C\'aceres, Jos\'e A. Ca\~nizo and St\'ephane Mischler
math.AP