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Matrix transformations and Walsh's equiconvergence theorem

Chikkanna R. Selvaraj, Suguna Selvaraj
2005 International Journal of Mathematics and Mathematical Sciences  
In 1977, Jacob definesGα, for any0≤α<∞, as the set of all complex sequencesxsuch that|xk|1/k≤α. In this paper, we applyGu−Gvmatrix 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 theGu−Gvmatrix transformation of the difference converges to zero in an arbitrarily large disk. Also, we give examples of such matrices.
doi:10.1155/ijmms.2005.2647 fatcat:75jz4oyptjaapbz4tdardx5qla