1. Nov 14, 2009

zetafunction

given two functions G and f (Real valued when their arguments are real) is it always possible to solve the equation

$$G(t-iu) + G(t+iu) = f(aut)$$

using Fourier transform with respect to 't' and using the common properties of Fourier transform i get (omitted constants)

$$G= \frac{1}{2|at|}\int_{-\infty}^{\infty}dw \frac{e^{iwt}}{cosh(uaw)}F(w)$$

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'