Two-loop self-energy contribution to the Lamb shift in H-like ions

The two-loop self-energy correction is evaluated to all orders in Z alpha for the ground-state Lamb shift of H-like ions with Z >= 10, where Z is the nuclear charge number and alpha is the fine-structure constant. The results obtained are compared with the analytical values for the Z alpha-expansion coefficients. An extrapolation of the all-order numerical results to Z=1 is presented and implications of our calculation for the hydrogen Lamb shift are discussed.