A new aspect of generalized integral operator and an estimation in a generalized function theory

Shrideh Al-Omari, Hassan Almusawa, nisar sooppy

Research output: Contribution to journalJournal articlepeer-review

Abstract

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 (Ben Salem and Ahmed Salem in Ramanujan J. 12(3):359–378, 2006) 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 δ and Δ convergences are also introduced.

Original languageEnglish
Article number357
JournalAdvances in Difference Equations
Volume2021
Issue number1
DOIs
StatePublished - Dec 2021

Keywords

  • Boehmian
  • Difference operator
  • Differential-difference function
  • Differential-difference operator
  • Integral transform
  • Jacobi–Dunkl function

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