Abstract view
Matrix transformations based on Dirichlet convolution


Published:19971201
Printed: Dec 1997
Chikkanna Selvaraj
Suguna Selvaraj
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 $\lim_{n\to \infty} \sum_{k\le n}
{1\over k}(f\ast x)(k) =L$, then $x$ is said to be {\it $A_f$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 $\ell  \ell$ and $GG$ mappings. The
strength of the $A_f$matrix is also discussed.