The Meijer transformation of generalized functions
This paper extends the Meijer transformation, Mμ, given by (Mμf)(p)=2pΓ(1+μ)∫0∞f(t)(pt)μ/2Kμ(2pt)dt, where f belongs to an appropriate function space, μ ϵ (−1,∞) and Kμ is the modified Bessel function of third kind of order μ, to certain generalized functions. A testing space is constructed so as t...
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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171287000334 |
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| _version_ | 1832545714065899520 |
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| author | E. L. Koh E. Y. Deeba M. A. Ali |
| author_facet | E. L. Koh E. Y. Deeba M. A. Ali |
| author_sort | E. L. Koh |
| collection | DOAJ |
| description | This paper extends the Meijer transformation, Mμ, given by
(Mμf)(p)=2pΓ(1+μ)∫0∞f(t)(pt)μ/2Kμ(2pt)dt,
where f belongs to an appropriate function space, μ ϵ (−1,∞) and Kμ is the modified Bessel function of third kind of order μ, to certain generalized functions. A testing space is constructed so as to contain the Kernel, (pt)μ/2Kμ(2pt), of the transformation. Some properties of the kernel, function space and its dual are derived. The generalized Meijer transform, M¯μf, is now defined on the dual space. This transform is shown to be analytic and an inversion theorem, in the distributional sense, is established. |
| format | Article |
| id | doaj-art-665a24a14e3b46e1936a89aa403d0d3c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-665a24a14e3b46e1936a89aa403d0d3c2025-02-03T07:24:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110226728610.1155/S0161171287000334The Meijer transformation of generalized functionsE. L. Koh0E. Y. Deeba1M. A. Ali2Department of Mathematics and Statistics, University of Regina, Regina S4S 0A2, CanadaDepartment of Applied Mathematical Sciences, University of Houston-Downtown, Houston, Texas 77002, USA#1598, Way 510, Muharraq 205, BahrainThis paper extends the Meijer transformation, Mμ, given by (Mμf)(p)=2pΓ(1+μ)∫0∞f(t)(pt)μ/2Kμ(2pt)dt, where f belongs to an appropriate function space, μ ϵ (−1,∞) and Kμ is the modified Bessel function of third kind of order μ, to certain generalized functions. A testing space is constructed so as to contain the Kernel, (pt)μ/2Kμ(2pt), of the transformation. Some properties of the kernel, function space and its dual are derived. The generalized Meijer transform, M¯μf, is now defined on the dual space. This transform is shown to be analytic and an inversion theorem, in the distributional sense, is established.http://dx.doi.org/10.1155/S0161171287000334Meijer transformgeneralized functionsBessel differential operatorSchwartz distributionsoperational calculus. |
| spellingShingle | E. L. Koh E. Y. Deeba M. A. Ali The Meijer transformation of generalized functions International Journal of Mathematics and Mathematical Sciences Meijer transform generalized functions Bessel differential operator Schwartz distributions operational calculus. |
| title | The Meijer transformation of generalized functions |
| title_full | The Meijer transformation of generalized functions |
| title_fullStr | The Meijer transformation of generalized functions |
| title_full_unstemmed | The Meijer transformation of generalized functions |
| title_short | The Meijer transformation of generalized functions |
| title_sort | meijer transformation of generalized functions |
| topic | Meijer transform generalized functions Bessel differential operator Schwartz distributions operational calculus. |
| url | http://dx.doi.org/10.1155/S0161171287000334 |
| work_keys_str_mv | AT elkoh themeijertransformationofgeneralizedfunctions AT eydeeba themeijertransformationofgeneralizedfunctions AT maali themeijertransformationofgeneralizedfunctions AT elkoh meijertransformationofgeneralizedfunctions AT eydeeba meijertransformationofgeneralizedfunctions AT maali meijertransformationofgeneralizedfunctions |