A new aspect of generalized integral operator and an estimation in a generalized function theory. (English) Zbl 1496.45013
Summary: In this paper we investigate certain integral operator involving Jacobi-Dunkl functions in a class of generalized functions. We utilize convolution products, approximating identities, and several axioms to allocate the desired spaces of generalized functions. The existing theory of the Jacobi-Dunkl integral operator [N. B. Salem and A. O. A. Salem, Ramanujan J. 12, No. 3, 359–378 (2006; Zbl 1122.44002)] is extended and applied to a new addressed set of Boehmians. Various embeddings and characteristics of the extended Jacobi-Dunkl operator are discussed. An inversion formula and certain convergence with respect to \(\delta\) and \(\Delta\) convergences are also introduced.
MSC:
| 45P05 | Integral operators |
| 47G10 | Integral operators |
| 39A70 | Difference operators |
| 39A12 | Discrete version of topics in analysis |
Keywords:
difference operator; differential-difference function; Jacobi-Dunkl function; integral transform; Boehmian; differential-difference operatorCitations:
Zbl 1122.44002References:
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