Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support

摘要

Let be the space of tempered distributions of Beurling type with test function space and let be the space of ultradifferentiable functions with arbitrary support having a period . We show that is generated by . Also, we show that the mapping is linear, onto, and continuous and the mapping is linear and onto where is the subspace of having a period and is the dual space of .