Matrix transformations and Walsh's equiconvergence theorem
In 1977, Jacob defines Gα, for any 0≤α<∞, as the set of all complex sequences x such that |xk|1/k≤α. In this paper, we apply Gu−Gv matrix transformation on the sequences of operators given in the famous Walsh's equiconvergence theorem, where we have that the difference of two sequences of op...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.2647 |
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| _version_ | 1832553692483551232 |
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| author | Chikkanna R. Selvaraj Suguna Selvaraj |
| author_facet | Chikkanna R. Selvaraj Suguna Selvaraj |
| author_sort | Chikkanna R. Selvaraj |
| collection | DOAJ |
| description | In 1977, Jacob defines Gα, for any 0≤α<∞, as the set of all complex sequences x such that |xk|1/k≤α. In this paper, we apply Gu−Gv matrix transformation on the sequences of operators given in the
famous Walsh's equiconvergence theorem, where we have that the
difference of two sequences of operators converges to zero in a
disk. We show that the Gu−Gv matrix transformation of the
difference converges to zero in an arbitrarily large disk. Also,
we give examples of such matrices. |
| format | Article |
| id | doaj-art-83d7e8e594c64b128dedd7a90fc8657e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-83d7e8e594c64b128dedd7a90fc8657e2025-02-03T05:53:31ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005162647265310.1155/IJMMS.2005.2647Matrix transformations and Walsh's equiconvergence theoremChikkanna R. Selvaraj0Suguna Selvaraj1Pennsylvania State University, Shenango Campus 147, Shenango Avenue Sharon, 16146, PA, USAPennsylvania State University, Shenango Campus 147, Shenango Avenue Sharon, 16146, PA, USAIn 1977, Jacob defines Gα, for any 0≤α<∞, as the set of all complex sequences x such that |xk|1/k≤α. In this paper, we apply Gu−Gv matrix transformation on the sequences of operators given in the famous Walsh's equiconvergence theorem, where we have that the difference of two sequences of operators converges to zero in a disk. We show that the Gu−Gv matrix transformation of the difference converges to zero in an arbitrarily large disk. Also, we give examples of such matrices.http://dx.doi.org/10.1155/IJMMS.2005.2647 |
| spellingShingle | Chikkanna R. Selvaraj Suguna Selvaraj Matrix transformations and Walsh's equiconvergence theorem International Journal of Mathematics and Mathematical Sciences |
| title | Matrix transformations and Walsh's equiconvergence theorem |
| title_full | Matrix transformations and Walsh's equiconvergence theorem |
| title_fullStr | Matrix transformations and Walsh's equiconvergence theorem |
| title_full_unstemmed | Matrix transformations and Walsh's equiconvergence theorem |
| title_short | Matrix transformations and Walsh's equiconvergence theorem |
| title_sort | matrix transformations and walsh s equiconvergence theorem |
| url | http://dx.doi.org/10.1155/IJMMS.2005.2647 |
| work_keys_str_mv | AT chikkannarselvaraj matrixtransformationsandwalshsequiconvergencetheorem AT sugunaselvaraj matrixtransformationsandwalshsequiconvergencetheorem |