Matrix transformations based on Dirichlet convolution

Chikkanna R. Selvaraj, Suguna Selvaraj

Research output: Contribution to journalArticle

Abstract

This paper is a study of summability methods that are based on Dirichlet convolution. If f(n) is a function on positive integers and x is a sequence such that limn→∞ Σk≤n 1/k(f * x)(k) = L, then x is said to be Af-summable to L. The necessary and sufficient condition for the matrix Af to preserve bounded variation of sequences is established. Also, the matrix Af is investigated as l - l and G - G mappings. The strength of the Af-matrix is also discussed.

Original languageEnglish (US)
Pages (from-to)498-508
Number of pages11
JournalCanadian Mathematical Bulletin
Volume40
Issue number4
StatePublished - Dec 1997

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Matrix Transformation
Dirichlet
Convolution
Bounded variation
Summability
Necessary Conditions
Integer
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Matrix transformations based on Dirichlet convolution. / Selvaraj, Chikkanna R.; Selvaraj, Suguna.

In: Canadian Mathematical Bulletin, Vol. 40, No. 4, 12.1997, p. 498-508.

Research output: Contribution to journalArticle

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