Abstract
Using the harmonic analysis associated to the Heckman–Opdam–Jacobi operator, relating to the root system \(BC_d\), we define and study the Wigner and Weyl transforms \(W_{\sigma }\) where \(\sigma \) is a symbol in \(S^m,m\in {\mathbb {R}}\). We give the connection between these transforms, and criterias in terms of the symbol \(\sigma \) to prove the boundedness and compactness of the transform \(W_{\sigma }\).
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Chettaoui, C., Hassini, A. & Trimèche, K. The Wigner and Weyl transforms attached to the Heckman–Opdam–Jacobi theory on \({\mathbb {R}}^{d+1}\). J. Pseudo-Differ. Oper. Appl. 12, 30 (2021). https://doi.org/10.1007/s11868-021-00404-z
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DOI: https://doi.org/10.1007/s11868-021-00404-z