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This article is cited in 1 scientific paper (total in 1 paper)
General numerical methods
On changing between bases of the space of representations of group $SO(2,2)$
I. Shilinab, J. Choic a National Research University "Moscow Power Engineering Institute", 111250, Moscow, Russia
b Moscow Sate Pedagogical University, 119991, Moscow, Russia
c Dongguk University, 38066 Gyeongju, Republic of Korea
Abstract:
Three bases of the space of representations are considered. Matrix elements of the transformation operators are found for each pair of these bases: for the first pair, they are represented in terms of the Gauss hypergeometric function, for the second pair by the product of Whittaker functions, and for the third pair in terms of the Bessel functions, Bessel–Clifford functions, or Meijer G-function. Using various approaches (Cartan decomposition, intertwining operator, or subrepresentation), formulas for special functions based on the matrix elements are derived.
Key words:
group $SO(2,2)$, matrix representation element, $_2F_1$, Whittaker function of the second kind, Bessel function of the second kind,
Bessel–Clifford function.
Received: 16.06.2020 Revised: 08.12.2020 Accepted: 09.04.2021
Citation:
I. Shilin, J. Choi, “On changing between bases of the space of representations of group $SO(2,2)$”, Zh. Vychisl. Mat. Mat. Fiz., 61:8 (2021), 1235–1244; Comput. Math. Math. Phys., 61:8 (2021), 1219–1228
Linking options:
https://www.mathnet.ru/eng/zvmmf11272 https://www.mathnet.ru/eng/zvmmf/v61/i8/p1235
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