Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the theory of the Kontorovich-Lebedev transformation on distributions

Authors: Semen B. Yakubovich and Brian Fisher
Journal: Proc. Amer. Math. Soc. 122 (1994), 773-777
MSC: Primary 46F12; Secondary 44A15
MathSciNet review: 1209431
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A new proof of the representation theorem for the Kontorovich-Lebedev transformation on distributions is given.

References [Enhancements On Off] (What's this?)

  • [1] Hans Bremermann, Distributions, complex variables, and Fourier transforms, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1965. MR 0208364
  • [2] Yu. A. \cyr{B}rychkov and A. P. \cyr{P}rudnikov, Integralnye preobrazovaniya obobshchennykh funktsii, Izdat. “Nauka”, Moscow, 1977 (Russian). Spravochnaya Matematicheskaya Biblioteka. [Mathematical Reference Library]. MR 0481945
  • [3] G. Buggle, Die Kontorovich-Lebedev-Transformation und die Mehler-Fok-Transformation für Klassen verallgemeinerter Functionen, Dissertation, TH Darmstadt, 1977.
  • [4] A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher transcendental functions, Vol. 2, McGraw-Hill, New York, 1953.
  • [5] G. Z. Forristall and J. D. Ingram, Evaluation of distributions useful in Kontorovich-Lebedev transform theory, SIAM J. Math. Anal. 3 (1972), 561–566. MR 0313805
  • [6] Hans-Jürgen Glaeske and Albrecht Hess, A convolution connected with the Kontorovich-Lebedev transform, Math. Z. 193 (1986), no. 1, 67–78. MR 852909, 10.1007/BF01163354
  • [7] N. N. Lebedev, Sur un formule d’inversion, C. R. (Doklady) Acad. Sci. URSS (N.S.) 52 (1946), 655–658 (French). MR 0021144
  • [8] A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and series. Vol. 2, Gordon & Breach Science Publishers, New York, 1986. Special functions; Translated from the Russian by N. M. Queen. MR 874987
  • [9] S. B. Yakubovich, The general integral transforms of the Kontorovich-Lebedev type and some of their applications, Ph.D. Dissertation, Minsk, 1987. (Russian)
  • [10] A. H. Zemanian, The Kontorovich-Lebedev transformation on distributions of compact support and its inversion, Math. Proc. Cambridge Philos. Soc. 77 (1975), 139–143. MR 0355489

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46F12, 44A15

Retrieve articles in all journals with MSC: 46F12, 44A15

Additional Information

Article copyright: © Copyright 1994 American Mathematical Society