Register to reply 
Solution to this equation 
Share this thread: 
#1
Jun410, 02:09 PM

P: 399

given any function (or maybe distribution) f(x) and g(x) so
[tex] f(x+i\epsilon )  f(xi\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
Jun410, 03:50 PM

Sci Advisor
P: 6,112

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. 


Register to reply 
Related Discussions  
Solution to Equation  General Math  2  
Solution of equation  Calculus & Beyond Homework  6  
Solution for equation  Precalculus Mathematics Homework  6  
Solution to Laplaces equation  Advanced Physics Homework  4  
Does this equation have any solution?  General Math  3 