Year: 2022
Author: Fida Bahba, Rabiaa Ghabi
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 4 : pp. 417–438
Abstract
In this paper we consider the Heckman-Opdam-Jacobi operator $∆_{HJ}$ on $\mathbb{R}^{d+1}.$ We define the Heckman-Opdam-Jacobi intertwining operator $V_{HJ},$ which turns out to be the transmutation operator between $∆_{HJ}$ and the Laplacian $∆_{d+1}.$ Next we construct $^tV_{HJ}$ the dual of this intertwining operator. We exploit these operators to develop a new harmonic analysis corresponding to $∆_{HJ}.$
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2019-0012
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 4 : pp. 417–438
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Heckman-Opdam-Jacobi operator generalized intertwining operator and its dual generalized Fourier transform generalized translation operators.