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What are the areas we can apply distributions in classical harmonic analysis? I don't mean probability distributions but distributions that are continuous linear functionals on the space of test functions. If I wish to venture into research about its applications through mathematical simulations or models or other things,what are the suggestions and helps do you have for me?

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    $\begingroup$ Fourier analysis of a constant signal gives you the Dirac delta function, is that a "real life" application? $\endgroup$
    – Carlo Beenakker
    Commented Feb 7, 2022 at 9:23
  • $\begingroup$ Green functions? $\endgroup$
    – Asaf
    Commented Feb 7, 2022 at 18:30

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