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1996 | 121 | 1 | 35-52
Tytuł artykułu

Hankel convolution on distribution spaces with exponential growth

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the Hankel transformation and Hankel convolution on spaces of distributions with exponential growth.
Czasopismo
Rocznik
Tom
121
Numer
1
Strony
35-52
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-11-20
poprawiono
1996-05-06
Twórcy
  • Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife, Islas Canarias, Spain, jbetancor@ull.es
  • Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife, Islas Canarias, Spain
Bibliografia
  • [1] J. J. Betancor, Characterization of Hankel transformable generalized functions, Internat. J. Math. Math. Sci. 14 (1991), 269-274.
  • [2] J. J. Betancor and B. J. González, A convolution operation for a distributional Hankel transformation, Studia Math. 117 (1995), 57-72.
  • [3] J. J. Betancor and I. Marrero, Multipliers of Hankel transformable generalized functions, Comment. Math. Univ. Carolin. 33 (1992), 389-401.
  • [4] J. J. Betancor and I. Marrero, The Hankel convolution and the Zemanian spaces $β_μ$ and $β_μ'$, Math. Nachr. 160 (1993), 277-298.
  • [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.
  • [6] J. J. Betancor and I. Marrero, Some properties of Hankel convolution operators, Canad. Math. Bull. 36 (1993), 398-406.
  • [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.
  • [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.
  • [9] F. M. Cholewinski, A Hankel convolution complex inversion theory, Mem. Amer. Math. Soc. 58 (1965).
  • [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.
  • [11] D. T. Haimo, Integral equations associated with Hankel convolutions, Trans. Amer. Math. Soc. 116 (1965), 330-375.
  • [12] M. Hasumi, Note on the n-dimensional tempered ultradistributions, Tôhoku Math. J. 13 (1961), 94-104.
  • [13] I. I. Hirschman, Jr., Variation diminishing Hankel transforms, J. Anal. Math. 8 (1960/61), 307-336.
  • [14] E. L. Koh and C. K. Li, The Hankel transformation on $M_μ'$ and its representation, Proc. Amer. Math. Soc. 122 (1994), 1085-1094.
  • [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.
  • [16] I. Marrero and J. J. Betancor, Hankel convolution of generalized functions, Rend. Mat. 15 (1995), 351-380.
  • [17] A. Pietsch, Nuclear Locally Convex Spaces, Springer, Berlin, 1972.
  • [18] F. Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967.
  • [19] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1956.
  • [20] K. Yoshinaga, On spaces of distributions of exponential growth, Bull. Kyushu Inst. Tech. Math. Natur. Sci. 6 (1960), 1-16.
  • [21] A. H. Zemanian, A distributional Hankel transform, SIAM J. Appl. Math. 14 (1966), 561-576.
  • [22] A. H. Zemanian, The Hankel transformation of certain distributions of rapid growth, ibid. 14 (1966), 678-690.
  • [23] A. H. Zemanian, Generalized Integral Transformations, Interscience Publ., New York, 1968.
  • [24] Z. Zielezny, On the space of convolution operators in $K_1'$, Studia Math. 31 (1968), 111-124.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv121i1p35bwm
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