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
DOI: https://doi.org/10.1090/S0002-9939-1994-1209431-0
MathSciNet review: 1209431
Full-text PDF

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] H. Bremermann, Distributions, complex variables and Fourier transforms, Addison Wesley, Reading, MA, 1965. MR 0208364 (34:8174)
  • [2] Yu. A. Brychkov and A. P. Prudnikov, Integral transforms of generalized functions, M. Nauka, 1977. MR 0481945 (58:2036)
  • [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 (47:2359)
  • [6] H. J. Glaeske and A. A. Heß, Convolution connected with Kontorovich-Lebedev transform, Math. Z. 193 (1986), 67-78. MR 852909 (87m:46085)
  • [7] N. N. Lebedev, Sur une formule d'inversion, Dokl. Akad. Nauk SSSR 52 (1946), 655-658. MR 0021144 (9:29d)
  • [8] A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 2, Gordon and Breach, New York, London, Paris, Montreux, and Tokyo, 1986. MR 874987 (88f:00014)
  • [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 (50:7963)

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

DOI: https://doi.org/10.1090/S0002-9939-1994-1209431-0
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society