A necessary condition that a function f(x) can be Fourier transformed is that f(x) is absolutely integrable. However, some function, such as |t|, still can be Fourier transformed and the result is 1/w^2, apart from some coefficients. This can be worked out, as we can add a exponential attenuation factor, and then send it to 0. In physics, we are always doing such things.(adsbygoogle = window.adsbygoogle || []).push({});

However, the inverse transform is not so apparent, the how to solve the inverse Fourier transform for 1/w^2? Indirectly, we have already know the result. but directly, how to solve this integral? Because we have a high order pole at the origin. It seems the divergence cannot be avoided.

I am confused with that.

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# Problems with Fourier transform

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