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- Problem Statement
- Let ##f:\mathbb R \to \mathbb C## be a smooth function such that ##|f| < C/(1+|x|^2)## for some ##C##. Put ##\phi(x) = \sum_{n = -\infty}^\infty f(x+n)##. Find Fourier coefficients of ##\phi## on [0,1] in terms of the Fourier transform of ##f##.

- Relevant Equations
- Fourier transform ##\hat f## of ##f## is ##\hat f(k) = 1/\sqrt{2\pi}\int_\mathbb R f(x) e^{-i k x}##

Hi PF!

Unsure how to begin. Fourier transform of ##f## I've given as an equation. I'm not sure what is meant by Fourier coefficients. Fourier coefficients of what?

Unsure how to begin. Fourier transform of ##f## I've given as an equation. I'm not sure what is meant by Fourier coefficients. Fourier coefficients of what?