| Title:
|
On tempered convolution operators (English) |
| Author:
|
Abdullah, Saleh |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
1-7 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
tempered distribution |
| Keyword:
|
convolution operator |
| Keyword:
|
Fourier transform |
| Keyword:
|
convergence of sequences |
| MSC:
|
46F05 |
| MSC:
|
46F10 |
| MSC:
|
46F12 |
| idZBL:
|
Zbl 0807.46036 |
| idMR:
|
MR1292577 |
| . |
| Date available:
|
2009-01-08T18:08:11Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118635 |
| . |
| Reference:
|
[1] Barros-Neto J.: An Introduction to the Theory of Distributions.Marcel Dekker, New York, 1973. Zbl 0512.46040, MR 0461128 |
| Reference:
|
[2] Grothendieck A.: Produits Tensoriels Topologiques et Espaces Nucleaires.Memoirs of the Amer. Math. Soc. 16, Providence, 1966. Zbl 0123.30301, MR 1609222 |
| Reference:
|
[3] Hörmander L.: On the division of distributions by polynomials.Ark. Mat., Band 3, No. 53 (1958), 555-568. MR 0124734 |
| Reference:
|
[4] Horvath J.: Topological Vector Spaces and Distributions.Vol. I, Addison-Wesley, Mass., 1966. Zbl 0143.15101, MR 0205028 |
| Reference:
|
[5] Keller K.: Some convergence properties of distributions.Studia Mathematica 77 (1983), 87-93. MR 0738046 |
| Reference:
|
[6] Schwartz L.: Théorie des Distributions.Hermann, Paris, 1966. Zbl 0962.46025, MR 0209834 |
| Reference:
|
[7] Sznajder S., Zielezny Z.: On some properties of convolution operators in $\mathscr{K}_{1}^{\prime}$ and $\mathscr{S}^{\prime}$.J. Math. Anal. Appl. 65 (1978), 543-554. MR 0510469 |
| . |
