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What is a derivative in the distribution sense?

  1. Aug 15, 2015 #1
    Never mind. I got this one. Couldn't figure out how to delete the post though.
     

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    Last edited: Aug 15, 2015
  2. jcsd
  3. Aug 15, 2015 #2

    micromass

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    Let ##u\in L^2(\mathbb{R})## be a function such that for all smooth ##\psi\in \mathcal{C}_c^1(\mathbb{R})##, we have that
    [tex]\int_{-\infty}^{+\infty} \psi(x) u(x)dx = -\int_{-\infty}^{+\infty} \psi'(x) \varphi(x)dx[/tex]
    Then ##u## is said to be the derivative of ##\varphi## in the distributional sense.
     
  4. Aug 15, 2015 #3
    Thanks, micromass! I had just found the answer and was editing the OP. Still much appreciated though.
     
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