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I have an equation $$ a\cdot \nabla u = a_1 \frac{\partial u}{\partial x_1} + a_2\frac{\partial u}{\partial x_2} + \cdots + a_n \frac{\partial u}{\partial x_n} = f(x). $$ Here $a_i$ are complex constants. The task is to find Green's function. I tried to do it using Fourrier transform but i failed to count an integral (I posted it here some time ago). Please help me to construct Green's function constructively (it's defined by $a\cdot \nabla_x G(x,y) = \delta(x-y))$.

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