Almost periodic at infinity functions from homogeneous spaces as solutions to differential equations with unbounded operator coefficients. (English) Zbl 1458.42009
Summary: By using the subspace of functions from homogeneous spaces with integrals decreasing at infinity we define new classes of functions almost periodic at infinity. We obtain spectral criteria for a function to be almost periodic at infinity and asymptotically almost periodic (with respect to the chosen subspace). These results are used for deriving criteria for almost periodicity at infinity of bounded solutions to differential equations with unbounded operator coefficients. In addition, for the new class of asymptotically finite-dimensional operator semigroups we prove the almost periodicity at infinity of their orbits.
MSC:
| 42A75 | Classical almost periodic functions, mean periodic functions |
| 43A60 | Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions |
Keywords:
almost periodic at infinity function; vanishing at infinity function; homogeneous space; Banach module; differential equations; asymptotically finite-dimensional operator semigroupReferences:
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