On the Time Average of the Autocorrelation Function in Hamiltonian   Dynamics
  Rigorous lower bound on the time-average of the autocorrelation function of an arbitrary L^1 observable is proven in terms of conserved quantities and ergodic decompositions of the Hamiltonian dynamics. Improvements with respect to the bounds given by Mazur and Suzuki are discussed. 
Pavle Saksida and Tomaz Prosen