Multidimensional Kontorovich–Lebedev transforms

Abstract

Different approaches are used to introduce a direct product Kontorovich–Lebedev transformation, its essentially multidimensional analogue and certain modifications in terms of multiple integrals over ℝ ⁿ ₊. Mapping properties are investigated. Inversion formulas are proved.

Keywords:

• Kontorovich–Lebedev transform
• modified Bessel functions
• Laplace transform
• Fourier transform
• Mellin transform
• Watson transforms
• multiple hypergeometric functions

AMS subject classification :

• 44A30
• 44A15
• 42B30
• 33C10
• 45A05
• 33C70

Acknowledgements

The present investigation was supported, in part, by the ‘Centro de Matemática’ of the University of Porto.