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

Yakubovich S. B., Vieira N.

Opuscula Mathematica

2011

Vol. 31, no. 1

137-146

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.

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

Yakubovich S. B.

Opuscula Mathematica

2009

Vol. 29, no. 3

313-329

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.