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Volume 38, Issue 4
Harmonic Analysis Associated with the Heckman-Opdam-Jacobi Operator on $\mathbb{R}^{d+1}$

Fida Bahba & Rabiaa Ghabi

DOI: 10.4208/ata.OA-2019-0012

Anal. Theory Appl., 38 (2022), pp. 417-438.

Published online: 2023-01

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  • 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 $∆_{HJ}.$

  • Keywords

Heckman-Opdam-Jacobi operator, generalized intertwining operator and its dual, generalized Fourier transform, generalized translation operators.

  • AMS Subject Headings

33E30, 42B10, 44A15, 35K05

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-38-417, author = {Bahba , Fida and Ghabi , Rabiaa}, title = {Harmonic Analysis Associated with the Heckman-Opdam-Jacobi Operator on $\mathbb{R}^{d+1}$}, journal = {Analysis in Theory and Applications}, year = {2023}, volume = {38}, number = {4}, pages = {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 $∆_{HJ}.$

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2019-0012}, url = {http://global-sci.org/intro/article_detail/ata/21357.html} }
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 $∆_{HJ}.$

Bahba , Fida and Ghabi , Rabiaa. (2023). Harmonic Analysis Associated with the Heckman-Opdam-Jacobi Operator on $\mathbb{R}^{d+1}$. Analysis in Theory and Applications. 38 (4). 417-438. doi:10.4208/ata.OA-2019-0012
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