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Matrix Transformations Based on Dirichlet Convolution

Published online by Cambridge University Press:  20 November 2018

Chikkanna Selvaraj  and
Suguna Selvaraj
Chikkanna Selvaraj
Affiliation:
Penn State University—Shenango Campus, 147, Shenango Avenue, Sharon, Pennsylvania 16146, U.S.A., e-mail: ulf@psuvm.psu.edu
Suguna Selvaraj
Affiliation:
Penn State University—Shenango Campus, 147, Shenango Avenue, Sharon, Pennsylvania 16146, U.S.A., e-mail: sxs32@psuvm.psu.edu
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Abstract

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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 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.

Keywords

11A2540A0540C0540D05

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 4 , 01 December 1997 , pp. 498 - 508
Copyright
Copyright © Canadian Mathematical Society 1997

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