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Keywords:
tempered distribution; convolution operator; Fourier transform; convergence of sequences
tempered distribution; convolution operator; Fourier transform; convergence of sequences
Summary:
\font\psaci=rsfs10 \font\ppsaci=rsfs7 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.
References:
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