RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Chebyshevskii Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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
Received: 04.09.2019
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}


Linking options:
  • http://mi.mathnet.ru/eng/cheb816
  • http://mi.mathnet.ru/eng/cheb/v20/i3/p349

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:12
    Full text:6

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020