A double index transform with a product of Macdonald's functions revisited

• Autorzy: Yakubovich S. B.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Macdonald function; index transforms; Kontorovich-Lebedev transform; double Mellin transform; Plancherel theorem; Parseval equality

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2009
• Tom: Vol. 29, no. 3
• Strony: 313--329
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Yakubovich S. B.

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

Bibliografia

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• [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.