On Vector Valued Periodic Distributions

In this paper we consider vector valued (X-valued with X a Banach space) distributions on the euclidean space Rd, extending the T-periodicity, and the T-periodic transform with T = (T1, …,Td) € Rd, Ti > 0 from the scalar case to the Banach space valued case.Besides immediate basic properties of these concepts, a realization of the space of X-valued T-periodic distributions, up to a toplinear isomorphism, as the space of all bounded linear operators from the space of T-periodic test functions to the Banach space X is given.