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from Part III - Discrete Functional Analysis
Published online by Cambridge University Press: 06 January 2022
Summability Theory deals with the assignment a sum to a divergent series or a limit to a divergent sequence. The basics of Summability Theory are given in this chapter. Cesaro Summability is studied in some detail. It is an example of a Matrix Summability Method. The Silverman–Toeplitz Theorem, which characterizes Matrix Summability Methods that sum all convergent series, is proven. Also, the Abel Summability Method, which is not a Matrix Summability Method, is studied.
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