Geodesic
On tempered convolution operators
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 1, pp. 1-7 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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\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.
\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.
Classification : 46F05, 46F10, 46F12
Keywords: tempered distribution; convolution operator; Fourier transform; convergence of sequences 
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     author = {Abdullah, Saleh},
     title = {On tempered convolution operators},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {1--7},
     year = {1994},
     volume = {35},
     number = {1},
     mrnumber = {1292577},
     zbl = {0807.46036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1994_35_1_a0/}
}
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Abdullah, Saleh. On tempered convolution operators. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 1, pp. 1-7. http://geodesic.mathdoc.fr/item/CMUC_1994_35_1_a0/