On the convergence in 𝒮’

Pilipović, Stevan

doi:10.1090/S0002-9939-1991-1050022-X

On the convergence in $\mathcal{S}'$

Author: Stevan Pilipović
Journal: Proc. Amer. Math. Soc. 111 (1991), 949-954
MSC: Primary 46F05
DOI: https://doi.org/10.1090/S0002-9939-1991-1050022-X
MathSciNet review: 1050022
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Abstract: We prove the following assertion: Let ${T_j},j \in \mathbb{N}$ , be a sequence in $\mathcal{S}'$ such that ${T_j} * \phi$ converges to 0 in $\mathcal{S}'$ as $j \to \infty$ , for any $\phi \in \mathcal{D}$ . Then ${T_j} \to 0$ in $\mathcal{S}'$ as $j \to \infty$ .

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