On the range of the Opdam–Cherednik transform and Roe’s theorem in the Cherednik setting

Mejjaoli, Hatem

doi:10.1007/s11868-015-0137-5

Cited by 3 publications

(2 citation statements)

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“…The Roe and the Paley-Wiener theorems in the context of Cherednik operators were established by using tempered distributions with spectral gaps in the Opdam-Cherednik operator (see, e.g., [14,15]). On the other hand, uncertainty principles and local uncertainty principles of Donoho-Strak type were derived by Achak and Daher [16].…”

Section: Introductionmentioning

confidence: 99%

“…Further, in an attractive perspective, they have adequately established certain analogs of Hardy, Beurling, Cowling-Price, Gelfand-Shilov and Miyachi theorems, with the aid of composition properties of the Opdam-Cherednik operator. However, various investigations and real applications of this integral operator may be observed in [11,12,[17][18][19][20] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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A new structure of an integral operator associated with trigonometric Dunkl settings

2021

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In this paper, we discuss a generalization to the Cherednik–Opdam integral operator to an abstract space of Boehmians. We introduce sets of Boehmians and establish delta sequences and certain class of convolution products. Then we prove that the extended Cherednik–Opdam integral operator is linear, bijective and continuous with respect to the convergence of the generalized spaces of Boehmians. Moreover, we derive embeddings and discuss properties of the generalized theory. Moreover, we obtain an inversion formula and provide several results.

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Section: Introductionmentioning

confidence: 99%