Saleh Abdullah
On tempered convolution operators

Comment.Math.Univ.Carolinae 35,1 (1994) 1-7.

Abstract:In this paper we show that if $S$ is a convolution operator in $\text {\ppsaci S}^{ \prime }$, and $S\ast \text {\ppsaci S}^{ \prime }=\text {\ppsaci S}^{ \prime }$, then the zeros of the Fourier transform of $S$ are of bounded order. Then we discuss relations between the topologies of the space $\text {\psaci O}_c^{ \prime }$ of convolution operators on $\text {\ppsaci S}^{ \prime }$. Finally, we give sufficient conditions for convergence in the space of convolution operators in $\text {\ppsaci S}^{ \prime }$ and in its dual.

Keywords: tempered distribution, convolution operator, Fourier transform, convergence of sequences
AMS Subject Classification: 46F05

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