(untitled) (Analysis in Theory and Applications, 2025)
We consider the notions of v-separation and (N,v)-separation for increasing sequences that tend to infinity. We study several of the connections between the properties of a multiplier in the space S'(R) and in other related spaces and the separation properties of the sequence of its zeros. We also prove that a distributional division problem Fh=f,always has tempered solutions h for any tempered data f if and only if the non integrable function 1/F admits regularizations that are tempered, and that this holds if and only if the pseudofunction P f (1/F) is tempered.