- #1
RedX
- 970
- 3
Suppose a function f(k) has a power series expansion:
[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.
[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.