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    Prasad, Akhilesh and Mandal, U. K. 2018. The Kontorovich–Lebedev Transform and Sobolev Type Space. Complex Analysis and Operator Theory, Vol. 12, Issue. 3, p. 669.
    Prasad, Akhilesh and Mandal, U. K. 2017. Wavelet transforms associated with the Kontorovich–Lebedev transform. International Journal of Wavelets, Multiresolution and Information Processing, Vol. 15, Issue. 02, p. 1750011.
    Prasad, Akhilesh and Mandal, U. K. 2016. Composition of pseudo-differential operators associated with Kontorovich–Lebedev transform. Integral Transforms and Special Functions, Vol. 27, Issue. 11, p. 878.
    Banerji, P. K. Loonker, Deshna and Kalla, S. L. 2009. Kontorovich–Lebedev transform for Boehmians. Integral Transforms and Special Functions, Vol. 20, Issue. 12, p. 905.
    Gutiérrez-Tovar, Y. E. and Méndez-Pérez, J. M. R. 2008. A convolution for the Hankel-Kontorovich-Lebedev transformation. Mathematische Nachrichten, Vol. 281, Issue. 11, p. 1566.
    Yakubovich, Semyon B. 2008. On a progress in the Kontorovich–Lebedev transform theory and related integral operators. Integral Transforms and Special Functions, Vol. 19, Issue. 7, p. 509.
    Gutiérrez-Tovar, Y.E. and Méndez-Pérez, J.M.R. 2007. The Kontorovich–Lebedev integral transformation with a Hankel function kernel in a space of generalized functions of doubly exponential descent. Journal of Mathematical Analysis and Applications, Vol. 328, Issue. 1, p. 359.
    Brychkov, Yu. A. and Prudnikov, A. P. 1986. Integral transforms of generalized functions. Journal of Soviet Mathematics, Vol. 34, Issue. 3, p. 1630.
    1985. Transmutation Theory and Applications. Vol. 117, Issue. , p. 323.
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The Kontorovich–Lebedev transformation on distributions of compact support and its inversion†

  • A. H. Zemanian (a1)
Extract

1. During the past decade a variety of integral transformations have been extended to various classes of distributions. However, one important integral transformation, which has defied such generalization, is the Kontorovich–Lebedev transformation. The objective of this note is to alter that situation.

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COPYRIGHT: © Cambridge Philosophical Society 1975
References
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(1)Lebedev, N. N.Sur une formule d'inversion. Dokl. Akad. Nauk SSSR (N.S.) 52 (1946), 655–658.
(2)Schwabtz, L.Théorie des distributions. Hermann; (Paris, 1966).
(3)Sneddon, I. N.The use of integral transforms. McGraw-Hill Book Co.; (New York, 1972).
(4)Zemanian, A. H.Generalized integral transformations. Interscience Publishers; (New York, 1968).
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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