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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the theory of the Kontorovich-Lebedev transformation on distributions
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by Semen B. Yakubovich and Brian Fisher
Proc. Amer. Math. Soc. 122 (1994), 773-777
DOI: https://doi.org/10.1090/S0002-9939-1994-1209431-0
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Abstract:

A new proof of the representation theorem for the Kontorovich-Lebedev transformation on distributions is given.
References
  • Hans Bremermann, Distributions, complex variables, and Fourier transforms, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1965. MR 0208364
  • Yu. A. Brychkov and A. P. Prudnikov, Integral′nye preobrazovaniya obobshchennykh funktsiĭ, Spravochnaya Matematicheskaya Biblioteka [Mathematical Reference Library], Izdat. “Nauka”, Moscow, 1977 (Russian). MR 0481945
    • G. Buggle, Die Kontorovich-Lebedev-Transformation und die Mehler-Fok-Transformation für Klassen verallgemeinerter Functionen, Dissertation, TH Darmstadt, 1977. A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher transcendental functions, Vol. 2, McGraw-Hill, New York, 1953.
  • 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 313805, DOI 10.1137/0503055
  • Hans-Jürgen Glaeske and Albrecht Hess, A convolution connected with the Kontorovich-Lebedev transform, Math. Z. 193 (1986), no. 1, 67–78. MR 852909, DOI 10.1007/BF01163354
  • N. N. Lebedev, Sur un formule d’inversion, C. R. (Doklady) Acad. Sci. URSS (N.S.) 52 (1946), 655–658 (French). MR 0021144
  • 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
    • S. B. Yakubovich, The general integral transforms of the Kontorovich-Lebedev type and some of their applications, Ph.D. Dissertation, Minsk, 1987. (Russian)
  • 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 355489, DOI 10.1017/S0305004100049471
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Bibliographic Information
  • © Copyright 1994 American Mathematical Society
  • 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