A Theory of Summability on a Space of Generalized Functions
A theory of summability of orthonormal sets is introduced in multinormed spaces. The approach which is presented caters for infinite sets , where the index set may be uncountable, and is applied to obtain convergence results in appropriate spaces of test functions and corresponding spaces of genera...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/384545 |
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| _version_ | 1832552306321653760 |
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| author | Khaula Naeem Khan Wilson Lamb |
| author_facet | Khaula Naeem Khan Wilson Lamb |
| author_sort | Khaula Naeem Khan |
| collection | DOAJ |
| description | A theory of summability of orthonormal sets is introduced in multinormed spaces. The approach which is presented caters for infinite sets , where the index set may be uncountable, and is applied to obtain convergence results in appropriate spaces of test functions and corresponding spaces of generalized functions. These spaces are constructed in a systematic manner that relies heavily on properties of orthonormal bases in Hilbert spaces. A space of almost-periodic generalized functions, in which each generalized function can be expanded in terms of an uncountable basis of exponential functions, is obtained as a special case of our theory. |
| format | Article |
| id | doaj-art-93915f301b2d48ae8d1deaabe489c35d |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-93915f301b2d48ae8d1deaabe489c35d2025-02-03T05:59:04ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/384545384545A Theory of Summability on a Space of Generalized FunctionsKhaula Naeem Khan0Wilson Lamb1Centre of Advanced Mathematics and Physics, National University of Sciences and Technology, Islamabad 44000, PakistanDepartment of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Livingston Tower, Glasgow G1 1XH, UKA theory of summability of orthonormal sets is introduced in multinormed spaces. The approach which is presented caters for infinite sets , where the index set may be uncountable, and is applied to obtain convergence results in appropriate spaces of test functions and corresponding spaces of generalized functions. These spaces are constructed in a systematic manner that relies heavily on properties of orthonormal bases in Hilbert spaces. A space of almost-periodic generalized functions, in which each generalized function can be expanded in terms of an uncountable basis of exponential functions, is obtained as a special case of our theory.http://dx.doi.org/10.1155/2013/384545 |
| spellingShingle | Khaula Naeem Khan Wilson Lamb A Theory of Summability on a Space of Generalized Functions Journal of Function Spaces and Applications |
| title | A Theory of Summability on a Space of Generalized Functions |
| title_full | A Theory of Summability on a Space of Generalized Functions |
| title_fullStr | A Theory of Summability on a Space of Generalized Functions |
| title_full_unstemmed | A Theory of Summability on a Space of Generalized Functions |
| title_short | A Theory of Summability on a Space of Generalized Functions |
| title_sort | theory of summability on a space of generalized functions |
| url | http://dx.doi.org/10.1155/2013/384545 |
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