Arithmetical summability

[摘要] The notation Sigma(k vertical bar n) f (k) means the finite sum of all numbers f (k) as k ranges over the integers that divide n including 1 and n. The purpose of this paper is to define a theory of summability suggested by this type of sum and an associated theory of convergence. This paper studies five sequence spaces that are related to the arithmetical summability thus defined. (C) 2012 Elsevier Inc. All rights reserved.

[发布日期] 2012-12-15

[关键词] Sequence space;Summability;Arithmetical sum;Mobius inversion