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1 - Background

from Part I - Tools and Theory

Published online by Cambridge University Press:  16 May 2024

Ariel Yadin
Ariel Yadin
Affiliation:
Ben-Gurion University of the Negev, Israel
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Summary

In this chapter all the basic notation and concepts are introduced.The notions of nilpotent, solvable, free, linear, finitely generated, and finitely presented groups are defined and examples are provided.Spaces of bounded and Lipschitz harmonic functions are defined, as well as harmonic functions of polynomial growths. Group actions are discussed and convolutions over abstract groups are defined.

Keywords

group actionconvolutionfinitely generated grouplinear groupfree groupnilpotent groupsolvable grouprandom walk on a groupharmonic functionCayley graph
Type
Chapter
Information
Harmonic Functions and Random Walks on Groups , pp. 3 - 49
Publisher: Cambridge University Press
Print publication year: 2024

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  • Background
  • Ariel Yadin, Ben-Gurion University of the Negev, Israel
  • Book: Harmonic Functions and Random Walks on Groups
  • Online publication: 16 May 2024
  • Chapter DOI: https://doi.org/10.1017/9781009128391.003
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  • Background
  • Ariel Yadin, Ben-Gurion University of the Negev, Israel
  • Book: Harmonic Functions and Random Walks on Groups
  • Online publication: 16 May 2024
  • Chapter DOI: https://doi.org/10.1017/9781009128391.003
Available formats
×

Save book to Google Drive

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.

  • Background
  • Ariel Yadin, Ben-Gurion University of the Negev, Israel
  • Book: Harmonic Functions and Random Walks on Groups
  • Online publication: 16 May 2024
  • Chapter DOI: https://doi.org/10.1017/9781009128391.003
Available formats
×