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

Abstract

Abstract 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.

Keywords

• Cherednik–Opdam integral operator
• Convolution product
• Polynomial
• Differential–difference operator
• Boehmian