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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.
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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