A convolution operation for a distributional Hankel transformation

J. Betancor; B. González

Studia Mathematica (1995)

  • Volume: 117, Issue: 1, page 57-72
  • ISSN: 0039-3223

Abstract

top
We investigate the Hankel transformation and the Hankel convolution on new spaces of generalized functions.

How to cite

top

Betancor, J., and González, B.. "A convolution operation for a distributional Hankel transformation." Studia Mathematica 117.1 (1995): 57-72. <http://eudml.org/doc/216241>.

@article{Betancor1995,
abstract = {We investigate the Hankel transformation and the Hankel convolution on new spaces of generalized functions.},
author = {Betancor, J., González, B.},
journal = {Studia Mathematica},
keywords = {Hankel transformation; convolution; distributions; Bessel functions; Hankel convolution; new spaces of generalized functions},
language = {eng},
number = {1},
pages = {57-72},
title = {A convolution operation for a distributional Hankel transformation},
url = {http://eudml.org/doc/216241},
volume = {117},
year = {1995},
}

TY - JOUR
AU - Betancor, J.
AU - González, B.
TI - A convolution operation for a distributional Hankel transformation
JO - Studia Mathematica
PY - 1995
VL - 117
IS - 1
SP - 57
EP - 72
AB - We investigate the Hankel transformation and the Hankel convolution on new spaces of generalized functions.
LA - eng
KW - Hankel transformation; convolution; distributions; Bessel functions; Hankel convolution; new spaces of generalized functions
UR - http://eudml.org/doc/216241
ER -

References

top
  1. [BM1] J. J. Betancor and I. Marrero, Multipliers of Hankel transformable generalized functions, Comment. Math. Univ. Carolin. 33 (1992), 389-401. Zbl0801.46047
  2. [BM2] J. J. Betancor and I. Marrero, The Hankel convolution and the Zemanian spaces β μ and β μ ' , Math. Nachr. 160 (1993), 277-298. 
  3. [BM3] J. J. Betancor and I. Marrero, Structure and convergence in certain spaces of distributions and the generalized Hankel convolution, Math. Japon. 160 (1993), 1141-1155. Zbl0795.46023
  4. [BM4] J. J. Betancor and I. Marrero, Some properties of Hankel convolution operators, Canad. Math. Bull. 36 (1993), 398-406. Zbl0795.46024
  5. [DP] L. S. Dube and J. N. Pandey, On the Hankel transform of distributions, Tôhoku Math. J. 27 (1975), 337-354. Zbl0331.46032
  6. [GN1] B. J. González and E. R. Negrin, Convolution over the spaces S k ' , J. Math. Anal. Appl. 190 (1995), 829-843. Zbl0827.46035
  7. [GN2] B. J. González and E. R. Negrin, Fourier transform over the spaces S k ' , ibid. 194 (1995), 780-798. 
  8. [H] D. T. Haimo, Integral equations associated with Hankel convolutions, Trans. Amer. Math. Soc. 116 (1965), 330-375. Zbl0135.33502
  9. [Hi] I. I. Hirschman, Jr., Variation diminishing Hankel transforms, J. Anal. Math. 8 (1960/61), 307-336. 
  10. [KL] E. L. Koh and C. K. Li, The complex Hankel transformation on M μ ' , Congr. Numer. 87 (1992), 145-151. 
  11. [KZ] E. L. Koh and A. H. Zemanian, The complex Hankel and I-transformations of generalized functions, SIAM J. Appl. Math. 16 (1968), 945-957. Zbl0167.41503
  12. [S] A. M. Sánchez, La transformación integral generalizada de Hankel-Schwartz, Ph.D. Thesis, Dep. Análisis Matemático, Universidad de La Laguna, 1987. 
  13. [W] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, London, 1958. 
  14. [Z1] A. H. Zemanian, The distributional Hankel transformation, SIAM J. Appl. Math. 14 (1966), 561-576. Zbl0154.13803
  15. [Z2] A. H. Zemanian, The Hankel transformation of certain distributions of rapid growth, ibid., 678-690. Zbl0154.13804
  16. [Z3] A. H. Zemanian, Generalized Integral Transformations, Interscience, New York, 1968. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.