A radial version of the Kontorovich-Lebedev transform in the unit ball

• Autorzy: Yakubovich S. B. , Vieira N.
• Języki publikacji: EN

Abstrakty

EN

In this paper we introduce a radial version of the Kontorovich-Lebedev transform in the unit ball. Mapping properties and an inversion formula are proved in Lp.

Słowa kluczowe

EN

Kontorovich-Lebedev transform; modified Bessel function; index transforms; Fourier integrals

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2011
• Tom: Vol. 31, no. 1
• Strony: 137--146
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Yakubovich S. B.

autor

Vieira N.

• University of Porto Faculty of Sciences Department of Pure Mathematics Rua do Campo Alegre st., 687, 4169-007 Porto, Portugal,

Bibliografia

• [1] G. Buggle, Die Kontorovich-Lebedev Transformation und die Mehler-Fok-Transformation für Klassen verallgemeinerter Fuctionen, Dissertation, TH Darmstad, 1977.
• [2] A. Erdelyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions, Volume 1, McGraw-Hill, 1953.
• [3] A. Erdelyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Tables of Integral transforms, Volume 2, McGraw-Hill, 1954.
• [4] M.I. Kontorovich, N.N. Lebedev, On the one method of solution for some problems in diffraction theory and related problems, J. Exper. Theor. Phys. 8 (1938) 10-11, 1192-1206 [in Russian].
• [5] N.N. Lebedev, Special functions and their applications, Prentice-Hall Inc., 1965.
• [6] N.N. Lebedev, I.P. Skal'skaya, Dual integral equations related to the Kontorovich-Lebedev transform, J. Appl. Math. Mech. 38 (1974) 6, 1033-1040 [in Russian].
• [7] J.S. Lowndes, An application of the Kontorovich-Lebedev transform, Proc. Edin. Math. Soc. 11 (1959) 3, 135-137.
• [8] S.K. Mukherjee, Advanced differential calculus on several variables, Academic Publisher, 2009.
• [9] D. Naylor, On a Lebedev expansion theorem, J. Math. Mech. 13, (1964), 353-363.
• [10] A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev, Integrals and Series, Volume 1: Elementary Functions, Gordon and Breach, 1986.
• [11] A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev, Integrals and Series, Volume 2: Special Functions, Gordon and Breach, 1986.
• [12] S. Yakubovich, Index transforms, World Scientific, 1996.
• [13] A.H. Zemanian, Generalized Integral Transform, McGray Hill: New York, 1965.