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1 results

  • 8 - Applications

  • from Part III - Discrete Functional Analysis
  • Martin Buntinas, Loyola University, Chicago
  • Book:
    Classical and Discrete Functional Analysis with Measure Theory
    Published online:
    06 January 2022
    Print publication:
    20 January 2022, pp 333-402

  • 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.