Abstract
1. At the recent International Congress I. M. Sheffer asked me the following question: Given a sequence {IS, }; form the sequence {an } of the Cesaro means of order a (a > 0) corresponding to { S, } . If S } is summable Abel, is it true that {a} is also summable Abel? A more general question is: Suppose that A and B are two regular summability methods for sequences {s,.} Denote by AB the iteration product which associates with a given sequence the A transform of its B transform; when does A summability imply AB summability? We shall show in ?2 that the answer is affirmative when B is (C, a) and A is Abel summability. I In ?3 we generalize this result to Laplace transforms and Riesz summability. In ?4 we discuss the iteration product of Cesaro and Borel summability, and also Euler and Borel summability.
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