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On tempered convolution operators. (English) Zbl 0807.46036
Summary: We show that if $$S$$ is a convolution operator in $${\mathcal S}'$$, and $$S*{\mathcal S}'= {\mathcal S}'$$, then the zeros of the Fourier transform of $$S$$ are of bounded order. Then we discuss relations between the topologies of the space $${\mathcal O}_ c'$$ of convolution operators on $${\mathcal S}'$$. Finally, we give sufficient conditions for convergence in the space of convolution operators in $${\mathcal S}'$$ and in its dual.
##### MSC:
 46F05 Topological linear spaces of test functions, distributions and ultradistributions 46F10 Operations with distributions and generalized functions 46F12 Integral transforms in distribution spaces
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