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

Advances in Difference Equations

article

Al-Omari, Shrideh¹  Almusawa, Hassan²  Nisar, Kottakkaran Sooppy³ 

[1] Department of Physics and Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University;Department of Mathematics, College of Sciences, Jazan University;Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University

关键词: Difference operator;    Differential-difference function;    Jacobi–Dunkl function;    Integral transform;    Boehmian;    Differential-difference operator;   

DOI  :  10.1186/s13662-021-03512-8

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY