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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |