# Article

Full entry | PDF   (0.2 MB)
Keywords:
multipliers; generalized functions; Hankel transformation
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.
References:
[1] Barros-Neto J.: An Introduction to the Theory of Distributions. R.E. Krieger Publishing Company, Malabar, Florida, 1981. Zbl 0512.46040
[2] Horvath J.: Topological Vector Spaces and Distributions, Vol. 1. Addison-Wesley, Reading, Massachusetts, 1966. MR 0205028
[3] Pietsch A.: Nuclear Locally Convex Spaces. Springer-Verlag, Berlin, 1972. MR 0350360 | Zbl 0308.47024
[4] Treves F.: Topological Vector Spaces, Distributions, and Kernels. Academic Press, New York, 1967. MR 0225131 | Zbl 1111.46001
[5] Wong Y.-Ch.: Schwartz Spaces, Nuclear Spaces, and Tensor Products. Lecture Notes in Math. 726, Springer-Verlag, Berlin, 1979. MR 0541034 | Zbl 0413.46001
[6] Zemanian A.H.: The Hankel transformation of certain distributions of rapid growth. SIAM J. Appl. Math. 14 (1966), 678-690. MR 0211211 | Zbl 0154.13804
[7] Zemanian A.H.: Generalized Integral Transformations. Interscience, New York, 1968. MR 0423007 | Zbl 0643.46029

Partner of