Suppose a function f(k) has a power series expansion:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f(k)=\Sigma a_i k^i [/tex]

Is it possible to inverse Fourier transform any such function?

For example:

[tex]f(k)=\Sigma a_i k^{i+2}\frac{1}{k^2} [/tex]

Since g(k)=1/k^2 should have a well-defined inverse Fourier transform, and the inverse Fourier transform of k*g(k) -> dg(x)/dx [where g(x) is the inverse Fourier transform of g(k)], then inverse Fourier transform of f(k) is an infinite sum of the inverse Fourier transforms of g(k)=1/k^2 and its derivatives d^n[g(x)]/dx^n.

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# Fourier transform

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