solution to this equation


by zetafunction
Tags: equation, solution
zetafunction
zetafunction is offline
#1
Jun4-10, 02:09 PM
P: 399
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]
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mathman
mathman is offline
#2
Jun4-10, 03:50 PM
Sci Advisor
P: 5,935
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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