Solution to this equation

  1. given any function (or maybe distribution) f(x) and g(x) so

    [tex] f(x+i\epsilon ) - f(x-i\epsilon ) = g(x) [/tex]

    if we know f(x) could we obtain g(x) from the difference above ??

    if we knew g(x) could we solve the equation to get f(x) ??

    here [tex] \epsilon \rightarrow 0 [/tex]
     
  2. jcsd
  3. mathman

    mathman 6,621
    Science Advisor
    Gold Member

    For the first question, if you know f(z) for all complex z, you can get g(x). For the second question the answer is no, since you can add any continuous function to f(z) and still get the same g(x).

    I presume that f(z) is discontinuous perpendicular to the real axis, otherwise the question is trivial.
     
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