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

Author: Stevan Pilipović
Journal: Proc. Amer. Math. Soc. 111 (1991), 949-954
MSC: Primary 46F05
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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Keywords: Tempered distributions
Article copyright: © Copyright 1991 American Mathematical Society