On the convergence in 𝒮’

Pilipović, Stevan

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

On the convergence in $\mathcal {S}’$
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by Stevan Pilipović

Proc. Amer. Math. Soc. 111 (1991), 949-954

DOI: https://doi.org/10.1090/S0002-9939-1991-1050022-X

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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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