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Given the equation

$ \Omega = a(x) \, + \langle \omega \mid \nabla_x \log \lambda(x) \rangle, $

where $x \in \mathbb{T}^n, \, a(x) > 0, \, \Omega > 0, \, \omega \in \mathbb{R}^n.$

I have to solve this equation for $\lambda(x)$ by using Fourier series.

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Is this homework? If so, please tag it as such. Also, what have you tried? –  Amzoti Dec 11 '12 at 16:06
    
I was thinking about writing $a(x) = \Sigma \, a_n \, e^{i2\pi n x}$ and $\lambda(x) = \Sigma \, l_n \, e^{i2\pi n x}$. –  simon Dec 11 '12 at 16:28

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