\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.
@article{118635,
author = {Saleh Abdullah},
title = {On tempered convolution operators},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {35},
year = {1994},
pages = {1-7},
zbl = {0807.46036},
mrnumber = {1292577},
language = {en},
url = {http://dml.mathdoc.fr/item/118635}
}
Abdullah, Saleh. On tempered convolution operators. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 1-7. http://gdmltest.u-ga.fr/item/118635/
An Introduction to the Theory of Distributions, Marcel Dekker, New York, 1973. | MR 0461128 | Zbl 0512.46040
Produits Tensoriels Topologiques et Espaces Nucleaires, Memoirs of the Amer. Math. Soc. 16, Providence, 1966. | MR 1609222 | Zbl 0123.30301
On the division of distributions by polynomials, Ark. Mat., Band 3, No. 53 (1958), 555-568. (1958) | MR 0124734
Topological Vector Spaces and Distributions, Vol. I, Addison-Wesley, Mass., 1966. | MR 0205028 | Zbl 0143.15101
Some convergence properties of distributions, Studia Mathematica 77 (1983), 87-93. (1983) | MR 0738046
Théorie des Distributions, Hermann, Paris, 1966. | MR 0209834 | Zbl 0962.46025
On some properties of convolution operators in $\mathscr{K}_{1}^{\prime}$ and $\mathscr{S}^{\prime}$, J. Math. Anal. Appl. 65 (1978), 543-554. (1978) | MR 0510469