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8 - Applications

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

Many applications of Functional Analysis are introduced, including Least Squares Approximation Methods, the Vibrating String or Membrane (the Wave Equation), Heat Flow on a rod or plate (the Heat Equation), Gambler's Ruin and Random Walk, Sampling Theorem of Signal Processing, the Atomic Theory of Matter, Uncertainty Principle, and Wavelets. The beautiful connection between Group Theory, Fourier Series, and the Haar Integral (which for Euclidean Space, is the Lebesgue Integral) is investigated.

Keywords

Least Squares MethodsWave EquationHeat EquationGambler's RuinRandom WalkBohr AtomSampling TheoremUncertainty PrincipleWaveletsHaar Integral
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Classical and Discrete Functional Analysis with Measure Theory , pp. 333 - 402
Publisher: Cambridge University Press
Print publication year: 2022

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  • Applications
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.013
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 Dropbox.

  • Applications
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.013
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.

  • Applications
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.013
Available formats
×