Hostname: page-component-74656f9884-npj9w Total loading time: 0 Render date: 2026-11-09T02:26:21.467Z Has data issue: false hasContentIssue false
  • English
  • Français

On Hankel convolutors on certain Hankel transformable function spaces

Published online by Cambridge University Press:  18 May 2009

Jorge J. Betancor  and
Lourdes Rodíguez-Mesa
Jorge J. Betancor
Affiliation:
Departamento De Análisis Matemático, Universidad De La Laguna, 38271-La Laguna, Tenerife Islas Canarias, EspaÑa, E-mail: jbetanco@ull.es
Lourdes Rodíguez-Mesa
Affiliation:
Departamento De Análisis Matemático, Universidad De La Laguna, 38271-La Laguna, Tenerife Islas Canarias, EspaÑa, E-mail: jbetanco@ull.es
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In this paper we introduce the spaces of Hankel convolutors. We characterize the dual spaces of certain Hankel transformable function spaces as spaces of Hankel convolutors. Here the Hankel convolution and the Hankel transformation play an important role.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 3 , September 1997 , pp. 351 - 369
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

REFERENCES

1.Betancor, J. J. and Marrero, I., Multipliers of Hankel transformable generalized functions, Comment. Math. Univ. Carolinae, 33(3) (1992), 389–401.Google Scholar
2.Betancor, J. J. and Marrero, I., The Hankel convolution and the Zemanian spaces βμ and β1μ, Math. Nachr., 160 (1993), 277–298.CrossRefGoogle Scholar
3.Betancor, J. J. and Marrero, I., Structure and convergence in certain spaces of distributions and the generalized Hankel convolution, Math. Japonica, 38(6) (1993), 1141–1155.Google Scholar
4.Betancor, J. J. and Marrero, I., Some properties of Hankel convolution operators, Canad. Math. Bull., 36(4) (1993), 398–406.CrossRefGoogle Scholar
5.Betancor, J. J. and Marrero, I., Algebraic characterization of convolution and multiplication operators on Hankel-transformable function and distribution spaces, Rocky Mountain J. Math., 25(4) (1995), 1189–1204.CrossRefGoogle Scholar
6.van Eijndhoven, S. J. L. and Kerkhof, M. J., The Hankel transformation and spaces of type W, Reports on Appl. and Num. Analysis, 10, Dept. of Maths, and Comp. Sci., Eindhoven University of Technology, (1988).Google Scholar
7.Gelfand, I. M. and Shilov, G. E., Generalized functions, Vol. 3 (Academic Press, New York, 1967).Google Scholar
8.Haimo, D. T., Integral equations associated with Hankel convolutions, Trans. Amer. Math. Soc., 116 (1965), 330–375.CrossRefGoogle Scholar
9.Hirschman, I. I. Jr, Variation diminishing Hankel transforms, J. Analyse Math., 8 (1960/1961), 307–336.CrossRefGoogle Scholar
10.Marrero, I. and Betancor, J. J., Hankel convolution of generalized functions, Rendiconti di Matematica, 15 (1995), 351–380.Google Scholar
11.Mikusinski, P. and Taylor, M. D., Toward a unified theory of generalized functions: convergence, Math. Nachr, 161 (1993), 27–43.CrossRefGoogle Scholar
12.Sánchez, A. M., La transformación integral generalizada de Hankel-Schwartz, Ph. D. Thesis (Departamento de Anólisis Matemaótico, Universidad de La Laguna, 1987).Google Scholar
13.Schwartz, A. L., Théorie des distributions (Hermann, Paris, 1978).Google Scholar
14.Zemanian, A. H., A distributional Hankel transformation, SIAM J. Appl. Math., 14 (1966), 561–576.CrossRefGoogle Scholar
15.Zemanian, A. H., The Hankel transformation of certain distributions of rapid growth, SIAM J. Appl. Math., 14 (1966), 678–690.CrossRefGoogle Scholar
16.Zemanian, A. H., Generalized integral transformations (Interscience Publishers, New York, 1968).Google Scholar