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Problem about analytic functions

by zetafunction
Tags: analytic, functions
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Nov14-09, 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(t-iu) + 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}{2|at|}\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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