Matrix transformations based on Dirichlet convolution

Chikkanna Selvaraj; Suguna Selvaraj

doi:10.4153/cmb-1997-059-6

Matrix transformations based on Dirichlet convolution

Chikkanna Selvaraj, Suguna Selvaraj

Penn State Shenango

Research output: Contribution to journal › Article › peer-review

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 lim_n→∞ Σ_k≤n 1/k(f * x)(k) = L, then x is said to be A_f-summable to L. The necessary and sufficient condition for the matrix A_f to preserve bounded variation of sequences is established. Also, the matrix A_f is investigated as l - l and G - G mappings. The strength of the A_f-matrix is also discussed.

Original language	English (US)
Pages (from-to)	498-508
Number of pages	11
Journal	Canadian Mathematical Bulletin
Volume	40
Issue number	4
DOIs	https://doi.org/10.4153/cmb-1997-059-6
State	Published - Dec 1997

All Science Journal Classification (ASJC) codes

General Mathematics

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Matrix transformations based on Dirichlet convolution

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