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 Chebyshevskii Sb., 2019, Volume 20, Issue 3, Pages 349–360 (Mi cheb816)

On one sum of Hankel–Clifford integral transforms of Whittaker functions

J. Choia, A. I. Nizhnikovb, I. Shilinb

a Dongguk University
b Moscow State Pedagogical University (Moscow)

Abstract: In [11], the authors considered the realization $T$ of $SO(2,2)$-representation in a space of homogeneous functions on $2\times4$-matrices. In this sequel, we aim to compute matrix elements of the identical operator $T(e)$ and representation operator $T(g)$ for an appropriate $g$ with respect to the mixed basis related to two different bases in the $SO(2,2)$-carrier space and evaluate some improper integrals involving a product of Bessel-Clifford and Whittaker functions. The obtained result can be rewritten in terms of Hankel-Clifford integral transforms and their analogue. The first and the second Hankel-Clifford transforms introduced by Hayek and Pérez–Robayna, respectively, play an important role in the theory of fractional order differential operators (see, e.g., [6, 8]). The similar result have been derived recently by the authors for the regular Coulomb function in [12].

Keywords: group $SO(2,2)$, matrix elements of representation, Hankel-Clifford integral transform, Macdonald-Clifford integral transform, Whittaker functions, Bessel-Clifford functions.

DOI: https://doi.org/10.22405/2226-8383-2018-20-3-349-360

Full text: PDF file (660 kB)

UDC: 517.444, 517.588
Accepted:12.11.2019
Language:

Citation: J. Choi, A. I. Nizhnikov, I. Shilin, “On one sum of Hankel–Clifford integral transforms of Whittaker functions”, Chebyshevskii Sb., 20:3 (2019), 349–360

Citation in format AMSBIB
\Bibitem{ChoNizShi19} \by J.~Choi, A.~I.~Nizhnikov, I.~Shilin \paper On one sum of Hankel--Clifford integral transforms of Whittaker functions \jour Chebyshevskii Sb. \yr 2019 \vol 20 \issue 3 \pages 349--360 \mathnet{http://mi.mathnet.ru/cheb816} \crossref{https://doi.org/10.22405/2226-8383-2018-20-3-349-360}