
#1
Nov1409, 06:49 AM

P: 399

given two functions G and f (Real valued when their arguments are real) is it always possible to solve the equation
[tex] G(tiu) + G(t+iu) = f(aut) [/tex] using Fourier transform with respect to 't' and using the common properties of Fourier transform i get (omitted constants) [tex] G= \frac{1}{2at}\int_{\infty}^{\infty}dw \frac{e^{iwt}}{cosh(uaw)}F(w) [/tex] in order to get a solution for G that depends on u and t (after integrating respect to w ) , here F(w) is the Fourier transform of f respect to 't' 


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