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Hankel Convolution Operators on Spaces of Entire Functions of Finite Order

Published online by Cambridge University Press:  20 November 2018

Jorge J. Betancor
Jorge J. Betancor*
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna. Tenerife, Islas Canarias, Spain e-mail: jbetanco@ull.es
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Abstract

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In this paper we study Hankel transforms and Hankel convolution operators on spaces of entire functions of finite order and their duals.

Keywords

46F12Hankel transformconvolutionentire functionsfinite order
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 2 , 01 June 2005 , pp. 161 - 174
Copyright
Copyright © Canadian Mathematical Society 2005

References

[1] Belhadj, M. and Betancor, J. J., Hankel convolution operators on entire functions and distributions. J. Math Anal. Appl. 276(2002), 40–63.Google Scholar
[2] Berenstein, C. A. and Gay, R., Complex variables, an introduction. Graduate Texts in Mathematics, 125, Springer-Verlag, New York, 1991.Google Scholar
[3] Betancor, J. J. and Bonilla, A., On the universality property of certain integral operators. J. Math. Anal. Appl. 250(2000), 162–180.Google Scholar
[4] Cholewinski, F. M. and Haimo, D. T., The Weierstrass-Hankel convolution. J. Analyse Math. 17(1966), 1–58.Google Scholar
[5] Ehrenpreis, L., Solution of some problems of division, III. Amer. J. Math. 78(1956), 685–715.Google Scholar
[6] van Eijndhoven, S. J. L. and Kerkhof, M. J., The Hankel transformation and spaces of type W. Reports on Appl. and Numer. Analysis, 10, Dept. of Maths. and Comp. Sci., Eindhoven University of Technology, 1988.Google Scholar
[7] Garnir, H. G., De Wilde, M., Schmets, J., Analyse fonctionnelle, Tome I. Birkhäuser Verlag, Basel, 1968.Google Scholar
[8] Haimo, D. T., Integral equations associated with Hankel convolutions. Trans. Amer. Math. Soc. 116(1965), 330–375.Google Scholar
[9] Hirschman, I. I. Jr., Variation diminishing Hankel transforms. J. Analyse Math. 8(1960/61), 307–336.Google Scholar
[10] Meise, R. and Vogt, D., Einführung in die Funktionalanalysis. Vieweg, Braunschweig, 1992.Google Scholar
[11] Watson, G. N., A treatise on the theory of Bessel functions. Cambridge University Press, Cambridge, 1995.Google Scholar
[12] Zemanian, A. H., Generalized integral transformations. Interscience Publishers, New York, 1968.Google Scholar