by zetafunction
Tags: analytic, functions
 P: 399 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'

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