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Abstrakty
We prove an inversion theorem for a double index transform, which is associated with the product of Macdonald's functions Kiτ (√x(2)+y(2)-y) Kiτ (√ x(2)+y(2)+y), where (x, y) ∈ R(+) x R(+) and iτ, τ ∈ R(+) is a pure imaginary index. The results obtained in the sequel are applied to find particular solutions of integral equations involving the square and the cube of the Macdonald function K(iτ) (t) as a kernel.
Czasopismo
Rocznik
Tom
Strony
313--329
Opis fizyczny
Bibliogr. 10 poz.
Twórcy
autor
- University of Porto Department of Pure Mathematics, Faculty of Science Campo Alegre st., 687 4169-007 Porto, Portugal, syakubov@fc.up.pt
Bibliografia
- [1] Yu.A. Brychkov, H-J.Glaeske, A.P.Prudnikov, V.K. Tuan, Multidimensional Integral Transformations, Gordon and Breach, Philadelphia, Paris, Tokyo, Melbourne, 1992.
- [2] A. Erd_elyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions, vols. I, II, McGraw-Hill, New York, London and Toronto, 1953.
- [3] N.N. Lebedev, On the representation of an arbitrary function by the integrals involving square of the Macdonald functions with the imaginary index, Sib. Mat. Journ. 3 (1962), 213-222.
- [4] N.T. Hai, S.B. Yakubovich, The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory, World Scientific, Singapore, 1992.
- [5] A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev, Integrals and Series: Special Functions, Gordon and Breach, New York, 1986.
- [6] I.N. Sneddon, The Use of Integral Transforms, McGray Hill, New York, 1972.
- [7] S.B. Yakubovich, Index Transforms, World Scientific, Singapore, 1996.
- [8] S.B. Yakubovich, On a new index transformation related to the product of Macdonald functions, Radovi Mat. 13 (2004), 63{85.
- [9] S.B. Yakubovich, The Plancherel and Hausdorff-Young type theorems for an index transformation, Journ. for Anal. and Appl. 25 (2006), 193-204.
- [10] S.B. Yakubovich, The Kontorovich-Lebedev transformation on Sobolev type spaces, Sarajevo Journ. of Math. 1 (2005) 14, 211-234.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHS-0001-0007