Convergence in spaces of rapidly increasing distributions.

Abdullah, Saleh

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In this paper we show that if $S$ is a convolution operator in $S^{'}$ , and $S * S^{'} = S^{'}$ , then the zeros of the Fourier transform of $S$ are of bounded order. Then we discuss relations between the topologies of the space $O_{c}^{'}$ of convolution operators on $S^{'}$ . Finally, we give sufficient conditions for convergence in the space of convolution operators in $S^{'}$ and in its dual.

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