Solutions Almost Periodic at Infinity to Differential Equations With Unbounded Operator Coefficients

The new class of functions almost periodic at infinity is defined using the subspace of functions with integrals decreasing at infinity. We obtain spectral criteria for almost periodicity at infinity of bounded solutions to differential equations with unbounded operator coefficients. For the new class of asymptotically finite operator semigroups we prove the almost periodicity at infinity of their orbits.