ThmDex – An index of mathematical definitions, results, and conjectures.

Processing math: 75%

Result R3166 on D4650: Vanishing function

Fourier transform of absolutely integrable function vanishes at infinity

Formulation 0

Let

$M = (\mathbb{R}^N, \mathcal{L}, \ell)$ be a D1744: Lebesgue measure space such that

(i)	$f : \mathbb{R}^N \to \mathbb{C}$ is an D1921: Absolutely integrable function on $M$

Then

$\begin{equation} \lim_{|\xi| \to \infty} \mathfrak{F}_f(\xi) = 0 \end{equation}$