Estimates of certain paraxial diffraction integral operator and its generalized properties
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 c...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-08-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02859-8 |
| _version_ | 1818428837240766464 |
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| author | Shrideh Al-Omari Serkan Araci Mohammed Al-Smadi Ghaleb Gumah Hussam Alrabaiah |
| author_facet | Shrideh Al-Omari Serkan Araci Mohammed Al-Smadi Ghaleb Gumah Hussam Alrabaiah |
| author_sort | Shrideh Al-Omari |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T15:07:58Z |
| format | Article |
| id | doaj.art-7a2bc0fda1e24d4dbfce9e46d4a6b056 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-14T15:07:58Z |
| publishDate | 2020-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-7a2bc0fda1e24d4dbfce9e46d4a6b0562022-12-21T22:56:39ZengSpringerOpenAdvances in Difference Equations1687-18472020-08-012020111110.1186/s13662-020-02859-8Estimates of certain paraxial diffraction integral operator and its generalized propertiesShrideh Al-Omari0Serkan Araci1Mohammed Al-Smadi2Ghaleb Gumah3Hussam Alrabaiah4Faculty of Engineering Technology, Al-Balqa Applied UniversityDepartment of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu UniversityDepartment of Applied Science, Ajloun College, Al-Balqa Applied UniversityFaculty of Engineering Technology, Al-Balqa Applied UniversityCollege of Engineering, Al Ain UniversityAbstract 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.http://link.springer.com/article/10.1186/s13662-020-02859-8Optical Fresnel integralParaxial diffraction integralFractional Fourier integralBoehmians |
| spellingShingle | Shrideh Al-Omari Serkan Araci Mohammed Al-Smadi Ghaleb Gumah Hussam Alrabaiah Estimates of certain paraxial diffraction integral operator and its generalized properties Advances in Difference Equations Optical Fresnel integral Paraxial diffraction integral Fractional Fourier integral Boehmians |
| title | Estimates of certain paraxial diffraction integral operator and its generalized properties |
| title_full | Estimates of certain paraxial diffraction integral operator and its generalized properties |
| title_fullStr | Estimates of certain paraxial diffraction integral operator and its generalized properties |
| title_full_unstemmed | Estimates of certain paraxial diffraction integral operator and its generalized properties |
| title_short | Estimates of certain paraxial diffraction integral operator and its generalized properties |
| title_sort | estimates of certain paraxial diffraction integral operator and its generalized properties |
| topic | Optical Fresnel integral Paraxial diffraction integral Fractional Fourier integral Boehmians |
| url | http://link.springer.com/article/10.1186/s13662-020-02859-8 |
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