1. Estimates of certain paraxial diffraction integral operator and its generalized properties.
- Author
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Al-Omari, Shrideh, Araci, Serkan, Al-Smadi, Mohammed, Gumah, Ghaleb, and Alrabaiah, Hussam
- Subjects
INTEGRAL operators ,GENERALIZED integrals ,THEORY of distributions (Functional analysis) ,FOURIER integrals ,MATHEMATICAL convolutions ,HYPERGEOMETRIC series - Abstract
This paper aims to discuss a generalization of certain paraxial diffraction integral operator in a class of generalized functions. At the start of this paper, we propose a convolution formula and establish certain convolution theorem. Then, with the addition to the convolution theorem, we consider a set of approximating identities and substantially employ our results in generating sets of integrable and locally integrable Boehmians. The said generalized integral operator is tested and declared to be one-to-one and onto mapping. Continuity of the generalized operator with respect to the convergence of the Boehmian spaces is obtained. Over and above, an inversion formula and consistency results are also counted. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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