TY - JOUR T1 - Harmonic Analysis Associated with the Heckman-Opdam-Jacobi Operator on $\mathbb{R}^{d+1}$ AU - Bahba , Fida AU - Ghabi , Rabiaa JO - Analysis in Theory and Applications VL - 4 SP - 417 EP - 438 PY - 2023 DA - 2023/01 SN - 38 DO - http://doi.org/10.4208/ata.OA-2019-0012 UR - https://global-sci.org/intro/article_detail/ata/21357.html KW - Heckman-Opdam-Jacobi operator, generalized intertwining operator and its dual, generalized Fourier transform, generalized translation operators. AB -

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 $∆_{HJ}.$