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# Solution to the Massive Laplacian Operator

Let $$\phi(x,y)$$ be the solution of the PDE: $$(-\Delta + m)\phi(x,y) = \delta(x-y)$$ where $$m > 0$$ and $$\Delta$$ is the usual $$d$$-dimensional Laplace operator. I’ve read that the solution of this equation can be written as: $$\phi(x,y) = \frac{1}{(2\pi)^{d}}\int e^{-ik(x-y)}(k^{2}+m^{2})^{-1}dk$$
but I’m having trouble proving it. The obvious way is to use Fourier transforms but I didn’t get too far. Can you help me, please?