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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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To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • 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
×