Bulletin of the Belgian Mathematical Society - Simon Stevin

The distributional Kontorovich-Lebedev transformation with the Hankel function in the kernel

Y. E. Gutiérrez-Tovar and J. M. R. Méndez-Pérez

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Abstract

A version of the Kontorovich-Lebedev transformation, involving the Hankel function of second kind in its kernel and connected with the Helmholtz's equation, has been investigated from a classical point of view by D. S. Jones. The main objective of this work is to extend this transform to certain space of generalized functions, establishing the corresponding distributional inversion formula.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 13, Number 3 (2006), 499-512.

Dates
First available in Project Euclid: 20 October 2006

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1161350691

Digital Object Identifier
doi:10.36045/bbms/1161350691

Mathematical Reviews number (MathSciNet)
MR2307685

Zentralblatt MATH identifier
1131.46030

Subjects
Primary: 46F12: Integral transforms in distribution spaces [See also 42-XX, 44-XX]

Keywords
Hankel function Kontorovich-Lebedev transformation inversion formula distributions

Citation

Gutiérrez-Tovar, Y. E.; Méndez-Pérez, J. M. R. The distributional Kontorovich-Lebedev transformation with the Hankel function in the kernel. Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 3, 499--512. doi:10.36045/bbms/1161350691. https://projecteuclid.org/euclid.bbms/1161350691


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