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11 - Summability

from Part III - Discrete Functional Analysis

Published online by Cambridge University Press:  06 January 2022

Martin Buntinas
Martin Buntinas
Affiliation:
Loyola University, Chicago
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Summary

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.

Keywords

SummabilityCesaro SummabilityMatrix SummabilityAbel SummabilitySilverman–Toeplitz
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Classical and Discrete Functional Analysis with Measure Theory , pp. 440 - 448
Publisher: Cambridge University Press
Print publication year: 2022

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  • Summability
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.016
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  • Summability
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.016
Available formats
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  • Summability
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.016
Available formats
×