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.

中文翻译：

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与三角 Dunkl 设置相关的积分算子的新结构

在本文中，我们讨论了 Cherednik-Opdam 积分算子到 Boehmians 抽象空间的推广。我们引入了 Boehmians 集并建立了 delta 序列和某些类别的卷积产品。然后我们证明扩展的 Cherednik-Opdam 积分算子对于 Boehmians 的广义空间的收敛性是线性的、双射的和连续的。此外，我们推导出嵌入并讨论广义理论的性质。此外，我们获得了一个反演公式并提供了几个结果。