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Matrix transformations and Walsh's equiconvergence theorem

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  • Chikkanna R. Selvaraj
  • Suguna Selvaraj

Abstract

In 1977, Jacob defines G α , for any 0 ≤ α < ∞ , as the set of all complex sequences x such that | x k | 1 / k ≤ α . In this paper, we apply G u − G v 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 G u − G v matrix transformation of the difference converges to zero in an arbitrarily large disk. Also, we give examples of such matrices.

Suggested Citation

  • Chikkanna R. Selvaraj & Suguna Selvaraj, 2005. "Matrix transformations and Walsh's equiconvergence theorem," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-7, January.
    • Handle: RePEc:hin:jijmms:282804
    DOI: 10.1155/IJMMS.2005.2647
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