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 - <p style="text-align: justify;">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 $∆_{HJ}.$</p>