Hankel convolution on distribution spaces with exponential growth

Betancor, Jorge ; Rodríguez-Mesa, Lourdes

Studia Mathematica, Tome 119 (1996), p. 35-52 / Harvested from The Polish Digital Mathematics Library

Résumé

We study the Hankel transformation and Hankel convolution on spaces of distributions with exponential growth.

Détail

Publié le : 1996-01-01

Zbl 0862.46021

EUDML-ID : urn:eudml:doc:216341

Bibliographie

[00000] [1] J. J. Betancor, Characterization of Hankel transformable generalized functions, Internat. J. Math. Math. Sci. 14 (1991), 269-274. | Zbl 0745.46044

[00001] [2] J. J. Betancor and B. J. González, A convolution operation for a distributional Hankel transformation, Studia Math. 117 (1995), 57-72. | Zbl 0837.46029

[00002] [3] J. J. Betancor and I. Marrero, Multipliers of Hankel transformable generalized functions, Comment. Math. Univ. Carolin. 33 (1992), 389-401. | Zbl 0801.46047

[00003] [4] J. J. Betancor and I. Marrero, The Hankel convolution and the Zemanian spaces $β_μ$ and $β_μ^{\prime }$, Math. Nachr. 160 (1993), 277-298. | Zbl 0796.46023

[00004] [5] J. J. Betancor and I. Marrero, Structure and convergence in certain spaces of distributions and the generalized Hankel convolution, Math. Japon. 38 (1993), 1141-1155. | Zbl 0795.46023

[00005] [6] J. J. Betancor and I. Marrero, Some properties of Hankel convolution operators, Canad. Math. Bull. 36 (1993), 398-406. | Zbl 0795.46024

[00006] [7] J. J. Betancor and I. Marrero, On the topology of Hankel multipliers and of Hankel convolution operators, Rend. Circ. Mat. Palermo (2) 44 (1995), 469-478. | Zbl 0859.46026

[00007] [8] J. J. Betancor and I. Marrero, Algebraic characterization of convolution and multiplication operators on Hankel-transformable function and distribution spaces, Rocky Mountain J. Math. 25 (1995), 1189-1204. | Zbl 0853.46034

[00008] [9] F. M. Cholewinski, A Hankel convolution complex inversion theory, Mem. Amer. Math. Soc. 58 (1965). | Zbl 0137.30901

[00009] [10] S. J. L. van Eijndhoven and M. J. Kerkhof, 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.

[00010] [11] D. T. Haimo, Integral equations associated with Hankel convolutions, Trans. Amer. Math. Soc. 116 (1965), 330-375. | Zbl 0135.33502

[00011] [12] M. Hasumi, Note on the n-dimensional tempered ultradistributions, Tôhoku Math. J. 13 (1961), 94-104. | Zbl 0103.09201

[00012] [13] I. I. Hirschman, Jr., Variation diminishing Hankel transforms, J. Anal. Math. 8 (1960/61), 307-336. | Zbl 0099.31301

[00013] [14] E. L. Koh and C. K. Li, The Hankel transformation on $M_μ^{\prime }$ and its representation, Proc. Amer. Math. Soc. 122 (1994), 1085-1094. | Zbl 0826.46033

[00014] [15] E. L. Koh and A. H. Zemanian, The complex Hankel and I-transformations of generalized functions, SIAM J. Appl. Math. 16 (1968), 945-957. | Zbl 0167.41503

[00015] [16] I. Marrero and J. J. Betancor, Hankel convolution of generalized functions, Rend. Mat. 15 (1995), 351-380. | Zbl 0833.46026

[00016] [17] A. Pietsch, Nuclear Locally Convex Spaces, Springer, Berlin, 1972.

[00017] [18] F. Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967. | Zbl 0171.10402

[00018] [19] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1956.

[00019] [20] K. Yoshinaga, On spaces of distributions of exponential growth, Bull. Kyushu Inst. Tech. Math. Natur. Sci. 6 (1960), 1-16. | Zbl 0166.39803

[00020] [21] A. H. Zemanian, A distributional Hankel transform, SIAM J. Appl. Math. 14 (1966), 561-576. | Zbl 0154.13803

[00021] [22] A. H. Zemanian, The Hankel transformation of certain distributions of rapid growth, ibid. 14 (1966), 678-690. | Zbl 0154.13804

[00022] [23] A. H. Zemanian, Generalized Integral Transformations, Interscience Publ., New York, 1968.

[00023] [24] Z. Zielezny, On the space of convolution operators in $K_1^{\prime }$, Studia Math. 31 (1968), 111-124. | Zbl 0182.45603