Abstract

In essence, Bromwich's theorem for matrix transformations [1] provides sufficient conditions in order that a method of summation with infinite matrix of reference shall include CesAro summability, a method of summation with finite matrix of reference. Various additional proofs of this theorem may be found in the mathematical literature, the most recent one by Garabedian [2], and also a number of applications, notably by Moore [3], Morse [4], and Garabedian [5]. This paper involves transformations of the type

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