A property of L−L integral transformations
The main result of this paper is the result that the collection of all integral transformations of the form F(x)=∫0∞G(x,y)f(y)dy for all x≥0, where f(y) is defined on [0,∞) and G(x,y) defined on D={(x,y):x≥0, y≥0} has no identity transformation on L, where L is the space of functions that are Lebe...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171284000533 |
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| author | Yu Chuen Wei |
| author_facet | Yu Chuen Wei |
| author_sort | Yu Chuen Wei |
| collection | DOAJ |
| description | The main result of this paper is the result that the collection of all integral transformations of the form F(x)=∫0∞G(x,y)f(y)dy for all x≥0, where f(y) is defined on [0,∞) and G(x,y) defined on D={(x,y):x≥0, y≥0} has no identity transformation on L, where L is the space of functions that are Lebesgue integrable on [0,∞) with norm ‖f‖=∫0∞|f(x)|dx. That is to say, there is no G(x,y) defined on D such that for every f∈L, f(x)=∫0∞G(x,y)f(y)dy for almost all x≥0. In addition, this paper gives a theorem that is an improvement of a theorem that is proved by J. B. Tatchell (1953) and Sunonchi and Tsuchikura (1952). |
| format | Article |
| id | doaj-art-3ce4246eda7543a8ac9b5c3204d460b4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3ce4246eda7543a8ac9b5c3204d460b42025-02-03T01:21:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017349750110.1155/S0161171284000533A property of L−L integral transformationsYu Chuen Wei0Department of Mathematics, University of Wisconsin-Oshkosh, Oshkosh 54901, Wisconsin, USAThe main result of this paper is the result that the collection of all integral transformations of the form F(x)=∫0∞G(x,y)f(y)dy for all x≥0, where f(y) is defined on [0,∞) and G(x,y) defined on D={(x,y):x≥0, y≥0} has no identity transformation on L, where L is the space of functions that are Lebesgue integrable on [0,∞) with norm ‖f‖=∫0∞|f(x)|dx. That is to say, there is no G(x,y) defined on D such that for every f∈L, f(x)=∫0∞G(x,y)f(y)dy for almost all x≥0. In addition, this paper gives a theorem that is an improvement of a theorem that is proved by J. B. Tatchell (1953) and Sunonchi and Tsuchikura (1952).http://dx.doi.org/10.1155/S0161171284000533L−L integral transformationabsolutely continuity of integralsLebesgue measurableLebesgue points. |
| spellingShingle | Yu Chuen Wei A property of L−L integral transformations International Journal of Mathematics and Mathematical Sciences L−L integral transformation absolutely continuity of integrals Lebesgue measurable Lebesgue points. |
| title | A property of L−L integral transformations |
| title_full | A property of L−L integral transformations |
| title_fullStr | A property of L−L integral transformations |
| title_full_unstemmed | A property of L−L integral transformations |
| title_short | A property of L−L integral transformations |
| title_sort | property of l l integral transformations |
| topic | L−L integral transformation absolutely continuity of integrals Lebesgue measurable Lebesgue points. |
| url | http://dx.doi.org/10.1155/S0161171284000533 |
| work_keys_str_mv | AT yuchuenwei apropertyofllintegraltransformations AT yuchuenwei propertyofllintegraltransformations |