| Title:
|
Multipliers of Hankel transformable generalized functions (English) |
| Author:
|
Betancor, J. J. |
| Author:
|
Marrero, I. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1992 |
| Pages:
|
389-401 |
| . |
| Category:
|
math |
| . |
| Summary:
|
\font\jeden=rsfs10 Let $\Cal H_{\mu }$ be the Zemanian space of Hankel transformable functions, and let $\Cal H'_{\mu }$ be its dual space. In this paper $\Cal H_{\mu }$ is shown to be nuclear, hence Schwartz, Montel and reflexive. The space $\text{\jeden O}$, also introduced by Zemanian, is completely characterized as the set of multipliers of $\Cal H_{\mu }$ and of $\Cal H'_{\mu }$. Certain topologies are considered on $\Cal O$, and continuity properties of the multiplication operation with respect to those topologies are discussed. (English) |
| Keyword:
|
multipliers |
| Keyword:
|
generalized functions |
| Keyword:
|
Hankel transformation |
| MSC:
|
44A05 |
| MSC:
|
46A11 |
| MSC:
|
46F10 |
| MSC:
|
46F12 |
| idZBL:
|
Zbl 0801.46047 |
| idMR:
|
MR1209282 |
| . |
| Date available:
|
2009-01-08T17:56:46Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118508 |
| . |
| Reference:
|
[1] Barros-Neto J.: An Introduction to the Theory of Distributions.R.E. Krieger Publishing Company, Malabar, Florida, 1981. Zbl 0512.46040 |
| Reference:
|
[2] Horvath J.: Topological Vector Spaces and Distributions, Vol. 1.Addison-Wesley, Reading, Massachusetts, 1966. MR 0205028 |
| Reference:
|
[3] Pietsch A.: Nuclear Locally Convex Spaces.Springer-Verlag, Berlin, 1972. Zbl 0308.47024, MR 0350360 |
| Reference:
|
[4] Treves F.: Topological Vector Spaces, Distributions, and Kernels.Academic Press, New York, 1967. Zbl 1111.46001, MR 0225131 |
| Reference:
|
[5] Wong Y.-Ch.: Schwartz Spaces, Nuclear Spaces, and Tensor Products.Lecture Notes in Math. 726, Springer-Verlag, Berlin, 1979. Zbl 0413.46001, MR 0541034 |
| Reference:
|
[6] Zemanian A.H.: The Hankel transformation of certain distributions of rapid growth.SIAM J. Appl. Math. 14 (1966), 678-690. Zbl 0154.13804, MR 0211211 |
| Reference:
|
[7] Zemanian A.H.: Generalized Integral Transformations.Interscience, New York, 1968. Zbl 0643.46029, MR 0423007 |
| . |
